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It will be the space company's first mission beyond low Earth orbit and the first lunar mission to be launched from New Zealand.
Rocket Lab will be launching a satellite for Nasa, which is working on plans to send astronauts to the Moon again.
Dubbed the Artemis program, Nasa wants to land the first woman and first person of colour on the Moon, and establish a long-term presence there.
Rocket Lab spokesperson Morgan Bailey said the Capstone satellite that it would launch was a small pathfinding satellite.
It will test out the orbit and navigating technologies Nasa wants to eventually use for its mini-space station, Gateway, which astronauts will use as their base to descend to the lunar surface.
It was a significant mission for Rocket Lab to be involved in, Bailey said.
"This is the very first step in Nasa's plans to return humans to the surface of the Moon, something that we have not done since the 1970s."
A small launch vehicle, as used by Rocket Lab, has never been used to launch a mission to the Moon.
"This is not just significant for Rocket Lab but this is significant internationally," Bailey said.
"What it really means is that we are bringing down the cost and the complexity and the time of being able to conduct really big science with really small spacecraft."
The contract is valued at just under $10 million, which Rocket Lab said made it one of the most affordable lunar launches undertaken.