The MP for Southend West in Essex, was attacked at Belfairs Methodist Church in Leigh-on-Sea.
According to reports a man walked into his constituency surgery and stabbed the 69-year-old multiple times.
Police are understood to be at the scene with a post on social media from the force in Essex confirming that an arrest had been made.
In a statement, Essex Police said officers arrived at the scene in Eastwood Road North shortly after 12.05pm and arrested a man, with an air ambulance also at the scene.
Aerial footage showed multiple police officers outside Belfairs Methodist Church and an air ambulance remained at the scene.
The statement from police said: “We were called to reports of a stabbing in Eastwood Road North, LeighonSea shortly after 12.05pm today (Friday 15 October).
“Officers were on scene shortly after, arrested a man and recovered a knife. He is currently in custody.
“We are not looking for anyone else in connection with the incident and do not believe there is an ongoing threat to the wider public.
“We want to thank the public who alerted us to the incident so quickly.
“We need anyone who saw anything or has CCTV, dash cam or doorbell footage to contact us. If you have any information you can submit a report online at https://www.essex.police.uk or use the ‘Live Chat’ button to speak to an online operator between 7am-11pm.
“Please quote incident 445 of 15 October. You can also call us on 101 or contact Crimestoppers anonymously on 0800 555 111.”
A spokesman for his office in Westminster said: “The incident has happened. I don’t know what the incident is. We are still waiting.”
An eyewitness to the incident told PA: “We just saw all the police and the ambulances turning up, it was probably about half past 12 or just before then.
“I saw about two or three ambulances and then an undercover police car and other police cars going past.
“There’s usually people walking past, elderly people walking to the shops. We’ve still got no idea what’s going on, we’re not very busy on a Friday and no one has come in to talk to us about it.”
Another witness called the incident “very distressing” and described seeing someone being taken out of the building and put into the back of a police car, before he was asked to leave the area.
He told LBC “At that point obviously we knew something serious had happened.
“Within five minutes we’d been informed by someone who was actually in the building what had happened and apparently he (Sir David Amess) had been stabbed quite a few times. It‘s very distressing that’s for sure.”
Conservative MP and former party leader Sir Iain Duncan Smith tweeted: “My thoughts are with David Amess MP and his family at this awful time.
“Praying for a full recovery following this appalling, shocking news. This angry, violent behaviour cannot be tolerated in politics or any other walk of life…”
Labour Party leader Sir Keir Starmer tweeted: “Horrific and deeply shocking news.
“Thinking of David, his family and his staff.”
First Minister Nicola Sturgeon tweeted her support to Sir David Amess, writing: “Dreadful news. Wishing @amessd_southend a full and speedy recovery”.
The Jo Cox foundation also released a statement of social media writing: “The Jo Cox Foundation is 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.”
Brendan Cox, widower of late Labour MP Jo Cox, who was murdered in an attack in 2016, described the stabbing of Sir David Amess as “as cowardly as it gets”.
He tweeted: “Attacking our elected representatives is an attack on democracy itself. There is no excuse, no justification. It is as cowardly as it gets.”
East Ham MP Stephen Timms, who was stabbed at a constituency surgery in 2010, wrote on Twitter: “Appalled to hear of the attack on @amessd_southend today. I know him well and am thinking of him with very best wishes as we await further news.”
The Conservative MP has served as an MP for 38 years, initially in Basildon from 1983 before he took on his role representing Southend West from 1997.