The Conservative MP was reportedly stabbed as he met constituents at a regular surgery in Leigh-On-Sea, and a 25-year-old man has been arrested on suspicion of murder.
Police have recovered a knife and have said they are not looking for anyone else in connection with the incident.
Mr Amess’ death comes just five years after the murder of Jo Cox in 2016.
The Jo Cox Foundation, the charity set up in memory of the MP, has already said it was “horrified” by the stabbing.
Sir Edward Leigh, Gainsborough’s Conservative MP, took to Twitter to say: “Devastated at the cruel loss of my friend David with whom I entered Parliament together 38 years ago.
“We stood shoulder to shoulder on many campaigns. He only wanted to serve kindly the people of Essex. He will be greatly missed.”
In Lincolnshire, former Labour Lincoln MP Karen Lee said: “So sad to hear about Sir David Amess who I worked alongside in Westminster on the APPG for Fire Safety & Rescue.
“He was of course on the benches opposite, but was always friendly and kind. My thoughts and prayers are with his family, RIP.”
And a tweet from Coun Colin Davie said: “Absolutely dreadful news that MP David Amess has died from his injuries.
"I thought after Jo Cox’s senseless murder that people would recognise that the use of language in politics had to change. It hasn’t and another person serving his community has paid the ultimate price.”