Elgassim Seed Ahmed, Elwaleed Imam and Alaa Aldin al- Difana have lived for years in Saudi Arabia where they worked until their arrest in December 2016, said the human rights watchdog.
"They appear to have been detained at the request of the Sudanese authorities in relation to posts on social media expressing support for civil disobedience protests in Sudan late last year," it said.
The London-based watchdog said there were "serious fears" Saudi authorities could deport them to Sudan, describing the three men as "prisoners of conscience".
She urged Saudi authorities to "immediately and unconditionally" release the men.
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Amnesty said the Saudi ministry of interior yesterday informed the families Elgassim and Elwaleed that the two men and their families would be deported within days.
The family of the third man was told he had been transferred from a jail in southwestern Saudi Arabia to one in Riyadh "raising fears the authorities are also preparing to deport him soon," it said.
The authorities were determined at that time to avoid any repetition of unrest similar to one in 2013 which was also sparked by a fuel subsidy cut.
That unrest was suppressed only by a deadly crackdown that drew international condemnation.