A video published by the Mail appeared to show Amesbury, the MP for Runcorn and Helsby, hitting the man in the face and knocking him to the floor, before standing over him and aiming six more blows at his head.
The security camera footage also showed Amesbury shouting: "You won't threaten me again, will you?"
A Labour spokesperson said: "Mike Amesbury MP has been assisting Cheshire police with their inquiries following an incident on Friday night.
As these inquiries are now ongoing, the Labour party has administratively suspended Mr Amesbury's membership of the Labour party pending an investigation."
The move means he will not be counted as a Labour MP until further notice. Amesbury said in a statement on Saturday night: "Last night I was involved in an incident that took place after I felt threatened on the street following an evening with friends. This morning I contacted Cheshire police myself to report what happened during this incident.
"I will not be making further comment but will, of course, cooperate with any inquiries if required by Cheshire police." Cheshire police confirmed that a 55-year-old man had been voluntarily interviewed under caution in relation to the incident after officers were called to reports of an attack in the town of Frodsham at 2.48am on Saturday.
"He has since been released pending further inquiries," the force said.
Amesbury becomes the eighth MP to have the Labour whip suspended since the election in July, though the first to suffer such a fate because of allegations over their personal behaviour. The party suspended the whip from seven others in July after they defied the government in a vote over removing the two-child benefit cap.
Amesbury's suspension came 24 hours after footage first circulated of the aftermath of the event, which showed him shouting while bystanders expressed shock at what had happened.
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