Ezzat El-Reshiq, a member of the Hamas political bureau, said in a statement the official, Mohammad Al-Khodary, 83, whom Saudi authorities detained in 2019 along with dozens of others, was on board a plane heading to Jordan.
"I spoke to him and he is in good spirit. He hopes and he prays that the rest of his detained brothers be freed," said Reshiq.
There was no immediate reply from Saudi officials on a Reuters request for comment.
Hamas was formed in the 1980s as an offshoot of the pan-Arab Muslim Brotherhood but has more recently stressed its basis as a Palestinian liberation movement, in part to defuse Egyptian enmity and draw support from wealthy Arab states.
Saudi Arabia, the United Arab Emirates and Egypt have cracked down against the Brotherhood, which they view as a threat to their systems of rule.