Amnesty said Bajadi has been held since March 21, 2011, a day after he attended a protest in Riyadh by families of detainees.
He has been charged with harming the reputation of the state and having banned books in his possession, and been on trial since August at a special court set up to try terrorism and security-related offences, it said.
Bajadi is "a prisoner of conscience held solely for the peaceful exercise of his rights to freedom of expression, assembly and association," said Hassiba Hadj Sahraoui, deputy head of Amnesty's Middle East and North Africa programme.
"All charges against him should be dropped and he should be released immediately," Sahraoui said.
"His hunger strike makes his release all the more urgent as his health must be deteriorating with each day he refuses food and water."
ACPRA itself warned on Tuesday that "the interior ministry... carries full responsibility over the deteriorating health condition" of Bajadi.
Bajadi "stopped drinking water early Saturday... fainting four times in a row, which proves that his life is in danger and his death inevitable," the NGO said.
But interior ministry spokesman Mansur al-Turki denied to AFP that Bajadi is on hunger strike. "Bajadi is taking his meals regularly and is in good health," he said.
The rights group called for Bajadi's "immediate release," saying he must face a "fair public trial."
Last month, ACPRA said Bajadi was arrested after publicly revealing information about the alleged "death by torture of Yemeni citizen Sultan Abdo al-Duais" while in Saudi custody.