The video shows a man on the ground with several officers attempting to restrain him before he is struck three times.
It has been seen more than 60,000 times, with many comments suggesting the arrested man should press charges against Northants Police.
A police spokesman said: “We are aware of a video circulating on Facebook showing the arrest of a man in Corby.
“Officers were called to a report of an assault in George Street, Corby, at about 1.30am on Sunday, April 10.
“On attendance the man who was suspected of being involved in the assault ran from officers and resisted arrest.
“A number of attempts were made to arrest the man and this video shows the end of this process.
“The man was taken into custody and an investigation into the alleged assault concluded that no further action should be taken against him.
“Northamptonshire Police has not received a complaint from the man arrested in connection with this incident.
“If he does wish to make a complaint he can call 101 or fill out an online form.”