Laura Shepard Churchley (74) was one of six people who made the trip aboard a commercial spacecraft that Jeff Bezos' Blue Origin launched.
The sub-orbital flight allowed passengers to briefly experience zero gravity.
Blue Origin launched the flight in 2021, the third of its kind. It aims to be the first to launch a space tourism product.
Ms. Shepard Churchley's dad, who died in 1998 after his Mercury flight from Florida's Cape Canaveral took off on May 5, 1961.
Michael Strahan, a former NFL star and Good Morning America anchor, was on Saturday's flight along with four other paying customers.
This was the first time Blue Origin filled all six seats of its New Shepard rocket. It is also the reason why the rocket's name, the Blue Origin astronaut, was given.
After being delayed by strong winds for two days, the flight took off from the launch facility of the company near Van Horn, Texas.
The flight was similar to other rockets launched by the company and landed in Texas desert, where Mr Bezos welcomed the tourists.
It lasted just over 10 minutes, and reached an altitude around 62 miles (100 km), which was five minutes and 116 fewer than Alan Shepard’s first flight.
His daughter also brought along a small portion of his capsule and mementos from Apollo 14's 1971 trip to the moon.
Ms. Shepard Churchley stated, "I thought about Daddy coming to me and thought, oh my god he didn’t get to enjoy any part of what I’m getting to enjoy." He was busy. He was able to do it all by himself. ". ".
Prince William, who criticised Blue Origin and other space tourism companies, warned that they were causing "climate anxiety" in younger generations.
