When the other patient said the worker had hurt his leg, the worker allegedly picked up the patient from under the shoulders and shook him.
Both patients identified were elderly. Neither knew each other before entering the ward.
A spokesperson for the North West London University Trust said: “We can confirm that we recently received a complaint about an alleged assault that is said to have occurred a few weeks ago on one of our wards.
“We have acknowledged the complaint and are referring it to the Metropolitan police for investigation as we normally would in these circumstances.”
When asked to confirm a report had been made to them, the Metropolitan Police could not locate it.