Two Saudi astronauts are now expected to travel to the International Space Station on May 22, after the trip was postponed by two weeks.
They are part of the Axiom Space 2 mission, which also includes former Nasa astronaut Peggy Whitson and American pilot John Shoffner.
Nasa announced the target date on Saturday, and that a SpaceX Falcon 9 rocket would lift off from Florida at 1.37am GST (May 21, 5.37pm ET).
This will be about a 10-day trip to the orbiting laboratory and will be the first mission for Saudi Arabia's new astronaut programme.
They will join UAE astronaut Sultan Al Neyadi, who is on board the station for a six-month mission.
The trip for the kingdom comes nearly 40 years after it sent its first citizen, Prince Sultan bin Salman, into orbit on Nasa's Space Shuttle for a week-long stay.
Ms Barnawi will become the first Arab woman on the ISS. Egyptian engineer Sara Sabry became the first Arab woman in space when she travelled on a Blue Origin space tourism flight in August of last year.
Saudi Space Commission — the kingdom's space agency — is trying to establish a sustainable space programme this time.
Ms Barnawi and Mr Al Qarni could be the first of a long list of astronauts that Saudi Arabia hopes to recruit.
Mishaal Ashemimry, the microgravity research leader at the Saudi Space Commission, said last month that the kingdom is considering long-duration space missions.
“We do have a desire and a goal to have long-stay missions that will capitalise on that microgravity environment,” she said.
“That's essentially what we would like to do with this human space flight programme.
“In doing so, we will train many astronauts, we will engage a lot of local entities to do a lot of research.
“We will also strengthen our international research partnerships in work on microgravity that spans from human health to physical science.”
During this trip, the two Saudi astronauts will be carrying out several science experiments assigned to them by Saudi-based universities.