In a statement, the government slammed what it described as the "coup" by the Shiite group, which recently seized control of the presidential palace in Sanaa and attacked the presidential residence, prompting clashes that left several dead and injured.
It also blamed the Houthi group for "paralyzing the state and the country's political transition."
"The Houthis put the president, prime minister and several ministers under house arrest in an incident unprecedented in Yemen's political history," it added.
The government went on to accuse the Shiite group of making an attempt on Bahah's life, citing a shooting attack on his convoy earlier this month.
Last week, Sanaa was rocked by deadly clashes between Houthi militants and presidential guard units amid an apparent push by the former to consolidate control.
President Abd Rabbuh Mansour Hadi, for his part, tendered his resignation last week shortly after Bahah and his government did the same to protest the Houthis' takeover of the capital.
Hadi's resignation has yet to be accepted by parliament.
The Houthis seized control of Sanaa last September before moving on to establish control over other parts of the country.
The rise of the Houthis has pitted the Shiite group against local Sunni tribes and Al-Qaeda, the latter of which is said to remain active in the country.
Fractious Yemen has remained in the throes of turmoil since autocratic President Ali Abdullah Saleh stepped down in 2012 following a months-long popular uprising against his 33-year rule.