Witnesses compared the blast, which sent a plume of smoke hundreds of metres into the sky, to an earthquake.
The explosion occurred in the Faj Attan area of the capital, near the presidential compound.
A Saudi-led coalition bombing campaign has been targeting Yemen's Shia Houthi rebels since late March.
Local resident Adel Mansour told Reuters news agency it was largest explosion in more than three weeks of bombing by the coalition.
"My children are terrified and one of my relatives fainted because of the force of the blast."
Meanwhile, a BBC correspondent in the contested port city of Aden says its hospitals lack the supplies to treat patients.
Orla Guerin says medical teams in the city are complaining that patients are dying for lack of equipment. They have appealed for more antibiotics and bandages.
The Houthi rebels and their allies have been trying to capture Aden for weeks but have been held back by the air strikes and by forces of President Abedrabbo Mansour Hadi, who has fled Yemen for Saudi Arabia.
In a televised address on Monday, rebel leader Abdul Malik al-Houthi said Yemenis would never give in to the Saudis' "savage aggression".
The blast in Sanaa followed an air strike that hit an Oxfam humanitarian store in Saada, a Houthi stronghold in the north of the country.
The charity condemned the strike, saying it had provided the co-ordinates of its warehouses to the Saudis.
The UN says 150,000 people have been displaced by the latest fighting, and some 12 million are short of food.
At least 25 people were killed and 300 injured in Yemen's capital Sanaa after an air strike on a missile base caused a huge blast that flattened buildings.