"Can this be real? Where is this nursing home? How is the victim doing?" Trump tweeted. The man has been arrested and the 75-year-old is said to have escaped without serious injuries.
The attacker, who has not been named, is said to be a resident of the same care home, which also offers rehabilitation therapy.
It is believed he filmed the abuse himself on May 15.
A person who viewed the video called police, who visited the Westwood Nursing Centre. Staff were already aware of the video, which has raised concerns about a possible cover up.
The suspect has also reportedly posted another video showing the beating of a woman confined to a bed.
The man has been arrested and Detroit police are investigating.