Ten people were killed after militants from al-Qaeda in the Arabian Peninsula (AQAP) launched an attack on a stadium which was used by the Houthis as a training camp in the city of Al-Bayda.
Another eight Houthis died in an AQAP suicide car bombing attack on a gathering of the Shia Houthi group at a school in Az Zahir District in al-Bayda Governorate.
In separate development, at least nine Houthis were killed in a roadside bomb explosion in Az Zahir District.
AQAP has claimed responsibility for the attacks.
In September 2014, Yemen's Shiite Houthi militants took over the capital Sanaa, deploying their fighters to Yemen's southern and eastern regions, where the security situation remains tense due to ongoing clashes between the Houthis and AQAP militants.
The violence has already killed more than 400 people.