"The resignation is final," the source, who requested anonymity, told The Anadolu Agency.
According to the source, the move was prompted by "interference" by the Shiite Houthi group and its "non-abidance by agreements with the presidency and its refusal to withdraw from the presidential sites it has occupied over the past two days."
The move came one day after the government failed to hold its weekly meeting after Houthi militants took over all main government offices.
Bahah himself was only allowed to leave the presidential palace in Sanaa on Tuesday after being held by Houthi militants for three days.
Sanaa has been rocked by deadly clashes over the past few days between Houthi militants and presidential guard units near the presidential palace in Sanaa amid an apparent push by the former to consolidate their control over the fractious country.
Later on Thursday, the Yemeni presidency said the Houthis had vowed to vacate the presidential palace, dismantle checkpoints set up in Sanaa, and free a presidential aide detained earlier.
The Houthis seized Sanaa last September and have since moved to extend their control to other provinces.
Some Arab capitals accuse Shiite Iran of backing Yemen's ongoing Houthi insurgency.
Yemen has remained in a state of relative lawlessness since a popular uprising that erupted in 2011 forced autocratic President Ali Abdullah Saleh to step down one year later.