One of the bombs was placed near the home of Ismail al-Wazir, a professor at Sanaa University, state news agency Saba quoted the director general of the Sanaa police, Brigadier General Abdelrazzaq al-Mo'ayad, as saying.
Wazir, who is close to the Houthi group, escaped an assassination attempt in April when gunmen opened fire on his vehicle, killing two of his security guards.
No one has claimed responsibility for the April attack or Tuesday's bombings, but the Houthis have been fighting the al Qaeda militants and allied tribesmen since its gunmen captured Sanaa in September and forced the resignation of a government they had long accused of corruption, according to Reuters.
The blasts occurred early in the morning when only a few people were on the streets, witnesses said. One said he saw a man on a motorbike place the bomb outside his house and it exploded almost immediately.
Another bomb exploded when a member of the Popular Committees, a local force set up by the Houthis after they captured Sanaa, was trying to dismantle it, police said.
Several houses and some cars were damaged from the explosions.