Several children were reportedly among the dead in Friday’s early morning attack on the Faj Attan neighbourhood of Sanaa which reduced an apartment block to rubble.
The capital is controlled by Iranian-backed Houthi rebels, who have been battling the alliance since 2015.
The coalition accused the rebels of “setting up a command and communications centre in the middle of this residential area to use civilians as human shields”.
They said a review of the airstrike had found “a technical mistake was behind the accident”.
Spokesman Colonel Turki al Malki said the coalition “regrets the collateral damage caused by this involuntary accident and offers its condolences to the families and relatives of the victims”.
Witnesses said the strike had not targeted the apartment block where people were killed, but instead hit an empty building next to it that caused the flats to collapse.
It was the latest in a wave of deadly raids on residential areas blamed on the coalition.
The International Committee of the Red Cross condemned the attack as “outrageous”, while Amnesty International said the alliance had “rained down bombs on civilians while they slept”.
The Houthis, who have controlled the capital since 2014, are allied with troops loyal to former president Ali Abdullah Saleh.
Meanwhile, the Saudi-led coalition is trying to restore the internationally recognised government of Abd Rabbu Mansour Hadi to power.
Nearly 8,400 civilians have been killed and 47,800 wounded since the alliance intervened in the conflict in 2015, according to the World Health Organisation.
The country is dealing with a deadly cholera outbreak that has claimed nearly 2,000 lives and affected more than half a million people since late April.
A shortage of food has also pushed the country to the brink of famine and Unicef says 400,000 children are in need of “urgent life-saving food”.