A man has been arrested and officers are not looking for anyone else, Essex Police said.
The extent of the 69-year-old MP's injuries are not yet known.
A statement from Essex 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.”
Yorkshire MP Yvette Cooper was among a number of serving MPs to react to the story. She tweeted: "This is truly dreadful. Thoughts and prayers with David."
The Jo Cox Foundation tweeted: "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."
Sir David was first elected as an MP in 1983, when he served in Basildon.
He then became MP for Southend West where he has been in office since 1997.