The fighters were killed in the town of Uqab, in Saada province, on Wednesday,
In the neighbouring province of Omran, four soldiers and five Houthis were killed as the army continued its Scorched Earth operation against the group.
Abdul-Malek al-Houthi, the leader of the Houthi fighters, has threatened to expand attacks against the government across the country.
Hundreds of people have died in northern Yemen, with the UN estimating that 55,000 people, mostly women and children, have fled their homes since the army began its offensive on August 11.
The Houthi fighters are concentrated mainly in the Saada and Amran provinces.
They are known as Houthis after their late leader, Abdul-Malek's brother Hussein Badr Eddin al-Houthi, a Zaidi leader who was killed by the Yemeni army in September 2004.An offshoot of Shia Islam, the Zaidis are a minority in mainly Sunni Yemen but form the majority in the north. Only a small minority of Zaidis are in involved in the Houthi uprising.
The government accuses the Houthi fighters of seeking to restore the Zaidi Shia imamate which was overthrown in a 1962 coup that sparked eight years of civil war.
The Houthis say they are fighting to defend their community against government aggression and marginalisation.
Ali Abdullah Saleh, the Yemeni president, has brushed aside calls for dialogue.
Source: Al Jazeera (English)