The Royal Stoke University Hospital has been designated as a "gym" where players can train their characters and fans have been seen roaming the site.
A hospital spokesman said it was "unconcerned" as long as people played the game where it was safe.
It warned it would get the "gym" removed if fans misused the A&E unit.
"Clinical staff have stated categorically that no one should attempt to enter A&E to play the game," a spokesman said.
"Should problems arise from the public misusing A&E to play Pokemon Go then the trust will have no choice but to contact the game's developer and have the 'gym' removed."
More on this and other stories from Stoke and Staffordshire
Kevin Parker, associate chief nurse at the hospital, said he was "aware" of the game's popularity, but warned players to stay away from the "incredibly busy" A&E department.
He said: "We want the public to understand that anybody who visits the hospital solely to play the game will provide an unwanted distraction to the important work of the hospital."
However, Michelle Harris, the hospital's sustainability manager, said managers appreciated the positive aspects of the game
She said: "We recognise that the Pokemon Go game encourages walking and exercise, which is something that the trust is equally keen to promote."
A hospital has warned players of the smartphone app game Pokemon Go not to enter the accident and emergency unit while they hunt for virtual monsters.