Sir David Amess was attacked on Friday morning in his constituency.
In a statement, Essex police said: “A man has been arrested on suspicion murder after a man was stabbed in Leigh-on-Sea.
“We were called to an address in Eastwood Road North shortly after 12.05pm today (Friday 15 October).
“We attended and found a man injured.
“He was treated by emergency services but, sadly, died at the scene.
“A 25 year-old man was quickly arrested after officers arrived at the scene on suspicion of murder and a knife was recovered.
“He is currently in custody.
“We are not looking for anyone else in connection with this incident.”