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."

Mr Allenby, 43, says he may have been drugged before he was taken from the bar on Friday. He was helped back to his hotel by a retired military man.
"I didn't think I was going to survive this one," he told the AAP news agency.
The golfer had been planning to fly out of Hawaii after missing the cut at the US PGA Tour's Sony Open.
Local television said the incident was being investigated as second-degree robbery.
"I was separated from my friend in the bar after we had paid the tab at 22:48 (08:48 GMT) and he went to the bathroom and next thing you know I'm being dumped in a park miles away," he said.
He said a homeless woman spotted him being dumped from a car, after being robbed of his phone and wallet.
The military veteran paid for a taxi for him back to the hotel, he said.
Pictures shown on the Golf Channel showed Mr Allenby with cuts on his nose and forehead and bruising around his eye.
His caddie Mick Middlemo told the channel Mr Allenby woke up groggy with no initial recollection of what happened to him.
Allenby is ranked 271 in the world and has won four titles on the elite PGA [Professional Golfers' Association] Tour.

The Redditch-based Sigma Financial Group has opened an office in Priory Queensway, in the city.
About 200 staff will be recruited by the end of this year with a further 500 expected by 2017, the firm has said.
"Roles will be spread across middle and senior management, contact centre staff and specialist commercial and finance jobs," said CEO Tim Freeman.
Sigma Financial Group is a business outsource firm. It employs more than 300 staff at its Prospect Hill base in Redditch.
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.
[NEXT_CONCEPT]
Australian golfer Robert Allenby says he was kidnapped from a bar in Hawaii, robbed and beaten, before being dumped in a park.
[NEXT_CONCEPT]
A finance company has announced plans to create more than 700 jobs in Birmingham before the end of next year.