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.

Stephen Gannon, 36, was assaulted on Broomfield Lane, near St Monance Street in the city's Springburn area, at about 17:20 on Friday.
Police Scotland said his attackers ran off in the direction of Balgrayhill Road. Mr Gannon died at the scene.
The death is being treated as murder and officers have appealed for information.
Det Ch Insp Allan Burton said: "Extensive inquiries are ongoing to try to establish the exact circumstances surrounding the incident.
"We have detectives from across the country assisting with the investigation and we will have additional uniformed officers in the area."

Jess Herbst, who became mayor of New Hope last May, made the announcement in an open letter to the town's residents.
"As your Mayor I must tell you about something that has been with me since my earliest memories. I am Transgender," she wrote.
Ms Herbst was appointed mayor following the death of her predecessor.
She had previously been elected to the Town Council as an alderman and road commissioner, according to her statement on the New Hope website.
"I know that transgender people are just coming to light in our society, and we have made great strides in the last few years," she said.
"My daughters have been adamant supporters of me and are proud to tell people their father is transgender," she added.
Ms Herbst has been documenting her experience on her blog, JessHerbst.com.
As the mayor of the small Collin County town, she is the first known openly transgender elected official in Texas history, the Texas Observer reports.
"I will continue as Mayor and hope to do the very best for the town," she said.
Transgender issues have made the headlines in Texas in recent months after Republicans unveiled the so-called "bathroom bill", a proposal that bans transgender people from using public bathrooms of their choice.
Such bills have become a flashpoint in the battle over transgender rights in the US.

In February, clubs agreed "in principle" to use the system from next season and those plans were confirmed at an EGM on 6 April.
Goalline technology has been used in the Premier League since 2013.
It has also been utilised in previous Football League play-off finals.
However, this season the technology will be available for both Championship semi-finals, as well as the final at Wembley on Monday, 29 May.
"The introduction of goalline technology is a significant step forward for Championship clubs and reflects the importance of the outcome of every single game in the division," said EFL chief executive Shaun Harvey.
"It has already proved successful elsewhere in our competitions and I'm confident it will have a similar positive impact week in, week out in the Championship, starting with this year's Championship play-off semi-finals."
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.
[NEXT_CONCEPT]
Detectives are looking for two men who left another man dying after a street attack in Glasgow.
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The mayor of a small town in Texas has become the first transgender elected official in the state's history, local media report.
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Goalline technology will be used in this season's Championship play-offs before being introduced in all second-tier matches in 2017-18, the English Football League has said.