The demonstrators chanted slogans against the government and demanded it step down over its recent decision to increase fuel prices.
Al-Houthi, the leader of the Shiite rebel Houthi movement, gave the government until Friday to revoke the price hikes or face what he called “a revolution.”
His supporters have pitched tents in a garden in the district of al-Jaraf in northern Sinai.
“We have set up these tents marking the start of the revolutionary escalation announced by the leader Abdel-Malek al-Houthi,” a spokesman for the protesters, Hazam al-Assad, told dpa.
“All our sit-ins inside Sana’a will be peaceful. We will not use weapons.”
The area houses headquarters of several ministries including those of interior, electricity and telecommunications.
Security has been tightened across Sana’a since early Friday, a day after President Abd Rabu Mansour Hadi ordered security forces to be on alert “for all possibilities.”
A presidential delegation was, meanwhile, meeting al-Houthi in his stronghold in the northern province of Saada to defuse the crisis.
The Houthis have expanded their influence from the far north and closer to Sana’a since the beginning of the year.
They have been locked in deadly fighting against Sunni rivals and government army troops in several areas of the country in recent months.
Yemen, the Arabian Peninsula’s most impoverished country, also faces a secessionist movement in the south and an insurgency by al-Qaeda operatives.