Officers said the 63-year-old victim suffered bruising to his face after he was "shoulder barged" in the road.
The video was shot on Thursday evening, after the opening day of the Grand National Festival, police said.
The 34-year-old suspect, from Formby, Merseyside, has been bailed.
In the mobile phone footage, which was posted on YouTube but has since been removed, a man is heard sniggering from behind the camera before the man falls to the ground.
Onlookers are then seen rushing to help the victim before calling for an ambulance.
Merseyside Police said the suspect later voluntarily attended a police station.
A spokesman said: "Merseyside Police has been made aware of a video showing a man shoulder-barging another, older man, over in a road near to the Aintree racecourse.
"The incident is being treated as assault and officers are speaking to several people believed to have further information that could help the investigation."
He added that officers plan to speak to the victim, who lives in Skelmersdale, Lancashire, later after making contact with a relative.
A man has been questioned over an alleged assault after a video emerged online of an Aintree racegoer appearing to deliberately knock a man to the ground.