One rescuer told AFP that at least 10 civilians were among the dead.
"Ten members of the same family were killed in the Al-Falihi neighbourhood, in Sanaa's old town," he said.
Residents said four houses were destroyed by a bomb and that 15 other buildings were damaged in the strikes.
Witnesses said five Iran-backed Huthi rebels were killed in a raid on their position in the capital, which the Shiite fighters seized unopposed last year.
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Residents of Sanaa's Al-Hassaba neighbourhood said coalition jets conducted several sorties overnight, targeting an interior ministry building and a police station.
A residence of ousted president Ali Abdullah Saleh, whose forces have allied with the Huthis, was also bombed, as well as an office of his political party, according to residents.
In Sanaa's central Zubeiri Street, an army communications office was hit for the first time by the coalition.
The insurgents still control the capital but have lost ground in the south since July when the coalition sent in armour, troops and Yemeni fighters trained in Saudi Arabia.
Riyadh formed the Arab alliance in response to fears the Huthis would take over all of Yemen and move it into the orbit of Sunni Saudi Arabia's Shiite regional rival Iran.
An analyst has estimated the coalition has more than 5,000 troops in Yemen, supporting local forces.
In Marib province, east of Sanaa, where pro-Hadi forces have launched a mass ground offensive, several Huthi positions were also bombed overnight, military sources said.
A Yemeni military source told AFP that General Fahd bin Turki, commander of Saudi-backed ground forces in Yemen, inspected troops deployed in Marib on Friday evening.
The United Nations says nearly 4,900 people have been killed since late March in Yemen, where the UN aid chief has called the scale of human suffering "almost incomprehensible.