Meanwhile, a Saudi-led coalition bombarded cities and towns in southern Yemen, as the targeted rebels accused it of killing 124 people on Monday in one of the deadliest days of its air war.
Yesterday's bloodshed came two days after UN envoy Ismail Ould Cheikh Ahmed arrived in Sanaa bidding to secure a humanitarian truce in a conflict estimated to have killed 3,000 people, mostly civilians.
The car bomb, at the al-Raoudh mosque in southeast Sanaa, went off as worshippers were leaving after evening prayers, witnesses and a security official said.
In a brief statement posted on jihadist websites, Islamic State said it had "taken revenge" against the Huthi rebels who have seized swathes of the country.
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Elsewhere on yesterday evening, four rebels were killed and 10 wounded in a suicide car bombing that targeted a police station in rebel-held Baida, in central Yemen, a security official and witnesses said.
Baida is a stronghold of al-Qaeda in the Arabian Peninsula (AQAP), also very active in southern and southeastern Yemen.
The capital of Sunni-majority Yemen has been under the control of the Iran-backed rebels since September.