Earlier this month, NASA awarded the contract, part of a programme aiming to return astronauts to the moon by 2024, to SpaceX over Blue Origin and defence contractor Dynetics.
NASA was expected to choose two of the three teams to competitively build lunar landers, making its selection of SpaceX as the sole winner a surprise.
"In NASA's own words, it has made a 'high risk' selection. Their decision eliminates opportunities for competition, significantly narrows the supply base, and not only delays, but also endangers America's return to the Moon," Blue Origin said in a statement cited by multiple US media outlets.
"Because of that, we've filed a protest with the [Government Accountability Office]," Blue Origin said.
The company claimed that the US space agency "executed a flawed acquisition for the Human Landing System program and moved the goalposts at the last minute," CNBC cited the statement as saying.
The SpaceX Starship, which is designed to land on the moon, is intended to eventually evolve into a fully reusable launch and landing system that can be used for space travel to destinations including the moon and Mars.
The mission will see four astronauts launched on NASA's Orion spacecraft into lunar orbit, where two of them - at least one of which a woman - will transfer to the SpaceX human landing system for their final journey to the moon.
The US brought 12 astronauts to the moon between 1969 and 1972.
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