Jasek, a member of a small Protestant Czech church called Cirkev Bratrska, had travelled to Sudan to help local Christians, according to Czech media reports.
Sudanese authorities said he had entered the country "illegally" from neighbouring South Sudan and gone to the conflict-riven state of South Kordofan.
In January, a court found him guilty of entering Sudan without a visa, spying, taking pictures of military installations and inciting hatred, according to his lawyer.
But Foreign Minister Ibrahim Ghandour announced on Sunday at a joint press conference with his visiting Czech counterpart Lubomir Zaoralek that Bashir had ordered Jasek's release.
Copyright Agence France-Presse, 2017