An undated handout photograph released by the UK Parliament shows Conservative MP for Southend West, David Amess, posing for an official portrait photograph at the Houses of Parliament in London.
Local police did not name Amess but confirmed that officers "were called to reports of a stabbing" shortly after 12:05 pm (1105 GMT).
"A man was arrested shortly after & we're not looking for anyone else," the force said on Twitter.
Sky News and the BBC identified the victim as the 69-year-old politician, from Prime Minister Boris Johnson's Conservative Party.
Amess was holding a his regular weekly meeting with constituents at the Belfairs Methodist Church, in the small town of Leigh-on-Sea.
He had advertised the event on his official Twitter account.
Conservative councillor and former Southend mayor John Lamb, who was at the scene, told local newspaper the Southend Echo: "All we know is that David has been stabbed several times.
"He is still at the church and they won't let us go in to see him. It does look very serious."
There was no immediate comment from Johnson, who was leading an away-day for senior ministers in the west of England.
But David Cameron, one of his Tory predecessors in Downing Street, 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".
An eye-witness, identified only as Anthony, told radio station LBC that the scene was "completely and utterly swamped by police, ambulance, armed police.
"I saw someone get taken out the building, put into the back of a police car. Apparently he was stabbed quite a few times."
Other British MPs have been attacked at similar constituency events, including Labour MP Jo Cox, who was murdered 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 on Sir David Amess MP.
"We are thinking of him, his family and loved ones at this distressing time," it added.
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.
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.