Last week's number one - The Secret Life of Pets - dropped to number two with takings of $29.3m (£22.3m).
Ghostbusters and Lights Out both took $21.6m (£16.4m) - making the two films tied in third place.
Ice Age: Collision Course debuted at number five with $21m (£15.9m), considerably lower than the previous films in the children's series.
All four of the animated movie's predecessors debuted with at least $40m (£30.4m) on their opening weekends.
Star Trek Beyond, which stars Chris Pine and Idris Elba, is the third film in the rebooted franchise.
But despite its strong performance in the US over the weekend,  it took $15m (£11.4m) less than 2009's Star Trek - the first film in the current series.
The film stars Anton Yelchin - who died earlier this year after a car accident in Los Angeles.
Hikaru Sulu, the character played by John Cho, is revealed to have a same sex partner in the film - a nod to George Takei, the gay actor who played the character in the original 1960s television series.
Other new entries in this week's US top 10 included Indian gangster film Kabali, which took $4.1m (£3.1m) to land at number eight.
Hillary's America: The Secret History of the Democratic Party, a documentary about presidential hopeful Hillary Clinton, debuted at number nine after taking $3.7m (£2.8m).
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Star Trek Beyond has topped the US box office chart after taking $59.9m (£45.6m) on its opening weekend.