The 22-second clip recorded from a high-rise building on Monday shows four officers kicking, hitting and stamping on the student as he lies on the ground.
The Kenyans recording the video can be heard expressing shock at the incident, with one of them letting out a cry as an officer kicks the student on the head.
The video ends with the student being led away by the policemen.
The police had been deployed to Jomo Kenyatta University of Agriculture and Technology (JKUAT) in Juja town, north of the capital, Nairobi, after students held a demonstration against rising insecurity, local media report.
The Inspector of Police Hilary Mutyambai, however, said in a statement on Tuesday that the officers were deployed to “restore order” after students blocked a major highway and started “harassing motorists and other road users”.
“It is important to note that all police officers have gone through a rigorous and professional training in management of riots and unlawful assemblies…the use of force must be legal and of necessity to the needs of justice,” he added.
The Minister for Interior Fred Matiang’i tweeted on Monday that action would be taken against the officers in 24 hours.
Mr Mutyambai said investigations had been opened and that any police officer found “culpable” would be held accountable.
The hashtag #StopPoliceBrutality is the top trending topic on Twitter, with tweeters sharing other videos of JKUAT students being attacked by police.
Officials at the university ordered the closure of the institution “indefinitely”.