Mr Amesbury said he would “co-operate with any investigation” after footage shared online appeared to show him swearing at a man lying in the road before a bystander pushed him.
Cheshire Police confirmed officers were called to reports of an assault in Frodsham at 2.48am and “inquiries are ongoing”.
Asked if the Labor Party was investigating, Ms Phillipson told Sky News’ Sunday Morning With Trevor Phillips programme: “Mike Amesbury, who is the MP in question, has gone to the police.
“He is cooperating with any investigation that they would like to pursue. This is a matter for the police and we want to let them do this job.
In a video shared on social media, the Runcorn and Helsby MP appears to point a finger at the man on the ground and say: “You’re never going to threaten me again, are you?” as someone off-camera shouts at him.
On Saturday, Mr Amesbury, 55, said: “Last night I was involved in an incident which happened after I felt threatened in the street after a night out with friends.
“This morning I contacted Cheshire Police to report what happened during the incident.
“I will not be making any further public comment but will of course assist with any investigation if requested by Cheshire Police.
“I remain fully committed to working hard for the people of Runcorn and Helsby and I am determined to remain an open and accessible MP for our community.”
Earlier on Friday, Mr Amesbury posted on social media that he was attending a meeting with local residents about policing and public safety.
In July last year, a 56-year-old man was convicted of stalking the MP at his constituency office in Frodsham, where prosecutors said he was seen looking through the glass and asked security about the level of security.
A Labor spokesman said the party was aware of the incident on Saturday and “we understand that (Mr Amesbury) has contacted Cheshire Police to report what happened this morning and that he will co-operate with any investigation they have’.
Cheshire Police said: “At 2.48am on October 26, police received a report of an assault in Frodsham.
“Caller reported being assaulted by a male on Main Street. Investigations are ongoing.”