Roads are closed and Charing Cross station is shut. Police manning the cordons say they may not be lifted for another four to five hours.
About 1,450 people were evacuated from a nightclub and hotel after the leak was discovered on Craven Street, just off Strand, shortly after 02:00 GMT.
A ruptured gas main has been detected, London Fire Brigade said.
The Metropolitan Police said it was working with the fire service and partner agencies to deal with the leak.
It tweeted: “A cordon and road closures are in place as a precaution and members of the public/motorists are advised to avoid the area at this time.”
A fire brigade spokesman said: “We are assisting police on the Strand after a ruptured gas main was discovered using detection equipment and high levels of natural gas were detected in the atmosphere.
“As a precaution, approximately 1,450 people have been evacuated. They are from a hotel and a night club.
“It is ongoing and engineers are down at the scene trying to isolate the leak. There are still high readings of natural gas in the area.
“We are working to sort it out as quickly as possible.”
From the scene: Marie Jackson, BBC News
It’s a wet start to the day in central London but it’s the road closures not the rain that’s causing big problems for many.
Fire engines line either side of the Strand and a 100m police cordon is in place. Police are letting a steady trickle of workers to cross, but there’s no way through for pedestrians along the Strand or down Northumberland Avenue.
Fire crews have been on the scene since 02:00 GMT. Station manager Brett Loft said 1,000 people had been evacuated from a club as well as Charing Cross hotel. He said it had been a “calm scene, with all going as we would like”.
His advice to commuters – seek an alternative route. “It’s difficult to say how long the cordons will stay up – we’re waiting for the gas authority to locate the leak,” he added.
A rest centre has been set up for affected residents at the Queen Mother’s Sport Centre in Vauxhall Bridge Road, Westminster Council said.
Revellers at the Heaven nightclub described trying to leave “as fast as possible”.
“Evacuated from heaven because of a gas leak, wow. Literally chaos. Crush on the stairs. Security being knocked aside,” one wrote on Twitter.
Another, Chloe-Mai, said: “Lots of people trying to leave at the same time. as soon as the word evacuation was heard from security staff everyone was trying to get out as fast as possible.”
Thani Spacey, a personal assistant at an office in the Strand, had just completed a 90-minute commute from Leigh-on-Sea in Essex to get to work early.
“I’m frustrated to say the least,” she said. “I’ve just had a text from work but why didn’t we hear earlier?”
Richard Okyere, 60, works as security officer on the Strand. He told the BBC he was in the building when he was alerted to a smell.
“My colleagues led me to the back of the building. The whole area smelt of gas, and we called the site engineers who came to investigate.”
BBC contributed to this report.