The human landing system (HLS) contract, worth $2.9 billion, was given to SpaceX, owned by Bezos's billionaire rival Elon Musk, in April.
It was protested by the other bidders, who argued NASA was required to make multiple awards and that the evaluation process was unfair.
"We firmly believe that the issues identified in this procurement and its outcomes must be addressed to restore fairness, create competition, and ensure a safe return to the Moon for America," Blue Origin said.
Since losing the contract, Blue Origin has strongly lobbied to have the decision reversed. It filed a protest with the Government Accountability Office, but in July the watchdog upheld NASA's decision.
NASA said in a statement Monday that it was notified of Blue Origin's lawsuit and it is reviewing the case.
"With our partners, we will go to the Moon and stay to enable science investigations, develop new technology, and create high paying jobs for the greater good and in preparation to send astronauts to Mars," the statement said.