Israel has beaten back its enemies. The war is now rocking its partners.

In a sign of the rising pressure, the Jordanian government on Wednesday effectively imposed a blanket ban on the Muslim Brotherhood, a Pan-Islamic political movement with significant influence in parts of the Arab world. Several members of the group were arrested earlier this month, accused of plotting attacks against Jordanian national security. The Brotherhood denied links to the alleged plots.

Frequent protests in the Jordanian capital, Amman, have included open criticism of the government and its relationship with Israel. Protesters have at times gathered near the U.S. and Israeli embassies, where they clashed with Jordanian forces.

While Egypt has maintained a tighter leash, it has occasionally allowed Egyptians to blow off steam in carefully managed demonstrations focused solely on solidarity with Palestinians—without criticism of the government of President Abdel Fattah Al Sisi.

The unrest poses a challenge to the leadership of the two Arab states, which are vital U.S. security partners in the region. Israel also relies on Cairo and Amman to crush nonstate armed groups and secure its longest borders. In Israel’s other neighbors, Lebanon and Syria, militant group Hezbollah and Palestinian factions have long held sway and used those countries to launch attacks on Israel.

The Jordanian monarchy and rule of Egypt’s Sisi sit in some of the most delicate—and uncomfortable—positions in the region. Sisi seized power in a coup that ousted a president backed by the Muslim Brotherhood.

After a series of wars between the 1940s and 1970s, Jordan and Egypt signed peace treaties with Israel in 1994 and 1979, respectively. That government-level peace brought trade, security and intelligence coordination as well as diplomatic ties, but it didn’t extend to broad swaths of the Jordanian and Egyptian public, which widely view Israel as hostile.

The war in Gaza has further strained that fragile, cold peace, as the Arab states have had to quell discontent among their populations while also maintaining and reaping economic and security benefits from their relations with Israel.

Some members of Israel’s right-wing government have pushed for moving Palestinians in the West Bank to Jordan, and Palestinians in Gaza to Egypt’s Sinai Peninsula. That has fueled popular anger over the war that has been simmering in those countries and prompted Amman and Cairo to confront Israel.

Jordanian police in Amman outside offices of the Muslim Brotherhood’s political arm, Islamic Action Front.

Egyptian officials have warned Israel that Cairo might go as far as suspending the 1979 peace treaty if Palestinians are pushed into Sinai. Jordan’s foreign minister has said it would be considered an act of war to displace Palestinians into Jordan.

“Jordan’s survival depends on what Israel does, and so does the Egyptian regime: If Israel drives Palestinians from Gaza into Sinai, and the regime fails to stem the tide, it could well fall," said Joost Hiltermann, special adviser at the Middle East program at International Crisis Group, a think tank. “And if Israel drives West Bank Palestinians into Jordan, this might well spell the end of the Kingdom of Jordan."

Egypt has accused Israel of violating their treaty by seizing a corridor along its border, and it has publicly beefed up its troop presence in the Sinai Peninsula. It has refused to approve the accreditation of Israel’s newly appointed ambassador to Egypt, and hasn’t dispatched a new ambassador to Israel. Sisi also refuses to talk to Israeli Prime Minister Benjamin Netanyahu by phone, according to Egyptian officials. Jordan for its part recalled its ambassador from Israel early in the war.

Israel is concerned about instability in Egypt, but especially in Jordan, which acts as a buffer to Iran and its proxies eastward, and it sees the stability of the kingdom as key for its own security. Both countries serve as important regional security partners for Israel.

A pro-Palestinian demonstration in Jordan in 2021. Millions of Jordanians are of Palestinian descent, and many support the Palestinian cause.

Millions of Jordanians are Palestinian descendants, and many express deep support for the Palestinian cause and even Hamas, which itself was born out of the Muslim Brotherhood in the 1980s.

The support also extends to the Muslim Brotherhood. Its affiliated political arm in Jordan, the Islamic Action Front, swept polls in the country’s parliamentary elections last year and now holds the largest bloc in the House of Representatives. The party’s future remains uncertain, as Jordan’s crackdown on the Brotherhood puts the country’s intolerance for the group in line with Saudi Arabia, the United Arab Emirates, Egypt and many other countries in the region.

“There can be no doubt that Israel’s war played a major role in mobilizing support" for the Islamic Action Front, said Neil Quilliam, associate fellow at the international affairs think tank Chatham House. “The result was a shock for the government."

Despite opposition from much of their populations, the Jordanian and Egyptian governments have quietly maintained their relationship with Israel through security coordination and trade, including energy and water, which is in short supply in Jordan.

Jordan, Egypt and Israel are consistently among the top five recipients of U.S. foreign funding in the world, and they maintain strong military ties with the U.S. Jordan hosts U.S. troops and last year helped America shoot down Iranian projectiles bound for Israel, garnering criticism in the monarchy.

In Egypt, like Jordan, the public “is fervently sympathetic with the people of Gaza," said Hiltermann, the Crisis Group analyst.

“Like elsewhere in the region, though, the regimes express this as well but hold a different view. The Egyptian government despises the Muslim Brotherhood, and therefore Hamas, and it needs Israeli support and technology," he added.

Still, Egypt has cracked down on Palestinian solidarity campaigns, fearing the activism could fuel dissent that spirals into demonstrations threatening the regime. Late last year, Egyptian criminal courts renewed the detention of more than 170 pro-Palestinian activists arrested in connection with protests.

In Jordan, the Muslim Brotherhood and its affiliates were some of the most prominent groups organizing frequent protests. The blanket ban against the group, which also prohibits attending or covering protests organized by it, brings Jordan closer to Egypt’s approach, analysts say.

“The Brotherhood has the capacity to mobilize the street, and that worries the government," said Hassan Abu Haniyeh, an expert on Islamic groups based in Amman.

“People want meaningful action—cutting ties (with Israel), sanctions, real consequences. But instead, the state is cracking down on the Brotherhood, either to scare people off or drive them away," he added.

Write to Omar Abdel-Baqui at omar.abdel-baqui@wsj.com and Summer Said at summer.said@wsj.com