Footage showed Amesbury punch Mr Fellows to the head, knocking him to the ground, then follow him onto the road and start to punch him again, at least five times.
Alison Storey, senior specialist prosecutor with the Crown Prosecution Service's special crime division, said: "This was a persistent assault by Mike Amesbury which continued while the victim was on the floor, offering no aggression.
The Runcorn and Helsby MP, who has been sitting as an independent since he was suspended following his arrest in October last year, had pleaded guilty earlier this year to assaulting 45-year-old Paul Fellows.
"After the initial punch which knocked the victim to the ground, Mike Amesbury struck the victim at least a further five times while he was on the floor.
Suspended Labour MP Mike Amesbury has been jailed for 10 weeks for punching a man following a row in the street, and taunting “you won’t threaten your MP again will you?”.