Two car bombs targeted mosques, while a third hit the house of the head of the Huthi rebels' politburo, Saleh al-Sammad, witnesses and security officials said.
Among the mosques hit by car bombs was Al-Hashush, which was targeted in March in a series of suicide bombings against Shiite houses of worship claimed by the Islamic state group that killed 142 people.
The other car bomb hit the Al-Quba Al-Khadra mosque in the central Hayel district, which is frequented by Huthi supporters.
Witnesses said the bombs were planted near the entrances to the mosques, and exploded as worshippers flocked in for the prayers, on the eve of the Muslim fasting month of Ramadan.
More From This Section
IS, a radical Sunni Muslim organisation, considers Shiites to be heretics
The Huthis overran Sanaa in September and have since expanded their control across several regions, aided by troops loyal to former president Ali Abdullah Saleh.
They pushed UN-backed President Abedrabbo Mansour Hadi into exile after advancing in March onto his refuge in the southern port city of Aden, triggering ongoing battles with southern fighters.
Today, the United Nations was scramblubg to get peace talks in Geneva moving, with the exiled government and the Iran-backed rebels accusing each other of trying to sabotage the process.