Dr Al Neyadi, his father, brothers and relatives received the President at their home in Al Ain's Umm Ghafa district.
The Emirati astronaut will join two American astronauts and a Russian cosmonaut aboard a SpaceX Falcon 9 rocket that will take off from Florida’s Kennedy Space Centre next spring.
Since graduating from Nasa’s astronaut basic training programme earlier this year, Dr Al Neyadi, 41, has been preparing for the mission in Houston, Texas, as well as at centres in Florida and California.
He returned briefly to his home town to brief Sheikh Mohamed about his training so far and the coming mission.
In a tweet, Dr Al Neyadi said the President's visit was “the absolute best motivation for me and all the people who work in the space sector in the UAE”.
“We promise you to do our best in representing our nation in the future space missions,” he said.
Sheikh Mohamed was accompanied by Sheikh Mansour bin Zayed, Deputy Prime Minister and Minister of the Presidential Court, and Sheikh Mohammed bin Hamad, special affairs adviser at the Presidential Court.
Images released by Emirates news agency Wam showed Dr Al Neyadi’s father seated next to Sheikh Mohamed, with Dr Al Neyadi briefing them using an iPad.
When Hazza Al Mansouri, the UAE’s first astronaut, returned from his eight-day stay on the ISS in 2019, he was received by Sheikh Mohamed, who accorded him a hero’s welcome.
Dr Al Neyadi was the back-up astronaut for the mission and returned to the UAE with Maj Al Mansouri.
Sheikh Mohamed said that the UAE would continue to make strides in modern science, artificial intelligence and advanced technology, Wam reported.
He also praised the determination Dr Al Neyadi has shown towards adding to the list of the UAE’s accomplishments.