Local authorities arrested a 25-year-old man at the scene on suspicion of murder and recovered a knife.
Sir David, a pro-Brexit MP and father-of-five first elected to parliament in 1983, was attacked inside the Belfairs Methodist Church while holding a fortnightly consultation with his local constituents in Leigh-on-Sea, east of London.
He was 69.
Prime Minister Boris Johnson was chairing a meeting with senior ministers in the west of England but promptly returned to London following news of the incident.
"The reason I think people are so shocked and saddened is above all he was one of the kindest, nicest, most gentle people in politics," he said of Sir David, calling him "a much-loved friend and colleague" and "a fine public servant".
Transport Secretary Grant Shapps called Sir David "a dedicated, thoughtful man and a true Parliamentarian, who lost his life while serving the constituents who he worked relentlessly for throughout his career".
Sir David is the latest British MP to have been attacked at his weekly constituency "surgery" with voters, which are typically held on Fridays when parliament is not sitting.
Pro-EU politician Labour MP Jo Cox was murdered by a far-right extremist in 2016 in the run-up to the Brexit referendum.
The Jo Cox Foundation, which was set up in her memory, tweeted that it was "horrified to hear the news of the attack".
"We are thinking of him, his family and loved ones at this distressing time," it added.
Ms Cox's widower Brendan described the stabbing of Sir David was "as cowardly as it gets".
"Attacking our elected representatives is an attack on democracy itself. There is no excuse, no justification."
Another Labour MP, Stephen Timms, was stabbed multiple times during an event in 2010, but recovered from "potentially life-threatening injuries" and is still an MP.
Mr Timms said he was "appalled" at the latest attack.
In January 2000, Liberal Democrat MP Nigel Jones was injured and his assistant killed by a man wielding a ceremonial sword at a constituency surgery in Cheltenham, western England.
Former Conservative leader Iain Duncan Smith expressed concern about the security risk of the local MP "surgeries".
"When you're not in your office, and you're in a public place... that means essentially, that the levels of security that sometimes you're advised to take can't be taken," he tweeted.
British MP stabbed to death at meeting with constituents
Sir David had advertised his upcoming surgery at the Belfairs Methodist Church in the small town of Leigh-on-Sea.
Paul Gardiner, 41, a barber at One Barbers Leigh-On-Sea, told AFP on Friday afternoon that "armed police and an ambulance" were on the scene.
"There's a couple of choppers around the place," he said.
Former prime minister David Cameron said: "Very alarming and worrying news reports coming from Leigh-on-Sea. My thoughts and prayers are with Sir David Amess and his family."
Opposition Labour leader Keir Starmer called the news "horrific and deeply shocking".