The city is largely in the hands of the Saudi-backed government forces, but has been a key battlefield in the conflict that has gripped Yemen since March 2015 as the rebels hold much of the surrounding countryside.
Last evening's shelling hit the residential neighbourhood of Al-Jamaliya, one of the oldest in the city, the official said.
It followed a similar bombardment on Friday which killed three children, two of whom were playing football at the time.
"What happened on Friday is yet another stark reminder of the immense suffering that civilians across Yemen are enduring in their daily lives," said ICRC regional director for the Near and Middle East Robert Mardini.
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"We urge all warring sides to take every precaution to spare civilians."
Human Rights Watch regretted the fact that the UN Human Rights Council had so far failed to agree on setting up an international inquiry into allegations of abuses by both the rebels, and the government and its backers in a Saudi-led coalition.
A spokesperson for the UN High Commissioner for Human Rights said the deaths "demonstrate the horrific impact on children and families, and all civilians, of the ongoing brutal war".
"Once again, we urge all sides to exercise restraint and to cease all indiscriminate attacks and take all possible precautions to properly distinguish military objectives from civilian objects," Robert Colville said.
More than 8,000 people, including at least 1,500 children, have been killed in Yemen since the coalition intervened in March 2015.
A cholera outbreak has claimed the lives of more than 1,800 people since April, with 400,000 suspected cases across the country, according to the UN and the ICRC.