The launch is the start of the Nusantara Satu mission for SpaceX involving an Indonesian communications satellite.
The 585-kilogram, dishwasher-sized lander was built by Israeli nonprofit space venture SpaceIL and state-owned defence contractor Israel Aerospace Industries (IAI) with $US100 million furnished nearly entirely by private donors.
Within an hour after liftoff, Beresheet was already sending back data and had successfully deployed its landing legs, according to SpaceIL.
"And you can't just jet straight off to the moon from Earth orbit, Winetraub said; the two celestial bodies must be lined up properly before Beresheet - whose name means "in the beginning" in Hebrew" - can make its move.
During a mission slated to last just two to three days on the moon, Beresheet will use on board instruments to photograph the landing site on the Sea of Tranquility, SpaceIL vice-president Yigal Harel said.
If Israel's space venture proceeds as planned, it will become the fourth - and by far the smallest - country to do so.
Beresheet is scheduled to reach the moon around April 4, then attempt a landing on April 11.
The $100 million Beresheet mission couldn't afford its own rocket - even a little one - so the organizers opted for a ride share. That makes for a much longer trip.
Other partners are Israel Aerospace Industries (IAI), Israel's space agency, and the country's Ministry of Science and Technology.
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The mission was originally intended for Google's Lunar Xprize, a competition created to encourage privately funded groups to send robotic landers to the moon.
The US Air Force also has a small research spacecraft aboard the rocket, for a one-year mission in orbit around Earth.
The Falcon 9 lifted off at 8:45 p.m.
A time capsule is aboard the lander - which includes a picture of Israeli astronaut Ilan Ramon, who died aboard space shuttle Columbia in 2003 - as well as a lunar library containing 30 million pages on a disk from the USA -based Arch Mission Foundation.
SpaceX plans to recover the first-stage booster, which flew twice past year, with a touchdown on an ocean platform.
The unmanned craft, weighing 1,300 pounds and standing approximately five feet tall, began an approximate seven-week journey to the moon, from where it will send back images of the rocky surface and conduct experiments on the lunar magnetic field. They were deployed shortly after, at 44 minutes after launch.
SpaceX has pioneered efforts to recover its rockets for reuse in future missions to dramatically cut costs.
According to SpaceX CEO Elon Musk, the booster could fly again as early as April in support of Crew Dragon's in-flight abort mission, although his implication that that test will occur in April directly contradicts a recent NASA schedule update that pegged the test no earlier than (NET) June 2019.