The Normacot Hotel has been sealed off while police investigate.
Officers are not looking for anyone else in connection with the incident which happened at the Normacot Hotel, Stoke-on-Trent, on Monday evening.
Tragic accident
Police said the girl was in a bedroom in a private area of the pub when the incident took place.
They have spoken to another child who was in the bedroom with the girl at the time and a weapon has been recovered.
Det Insp Wayne Jones said it appeared to be a tragic accident.
"We are still working to establish the circumstances which lead to the discharge of the weapon and we are working to support the family at this distressing time," he said.
What the hell is happening to this country?
Kid are out of control and rampaging all over the country while the police are busily investigating an 'accidental' airgun shooting. Why on earth do they think the pub needs to be sealed off?
I have noticed that van loads of armed coppers descend from on high at the mere mention of the word gun and rip the place apart whatever. Trouble is, the gun crime is on the streets.
When I was a kid and we accidentally shot one of our number the hospital told us to report it to the police, they didn't want to know and refused to accept any statements. 'It was an accident' 'What do you want us to do about it?' just about summed it up.
Are they now going to ban airguns? They've been dying to for ages. They have got to the stage of wanting to ban pictures of guns any yet gun crime has never been so high.
I defy anyone to watch an evenings telly without seeing guns in action by most everyone in the world and they think banning is the answer!