Firefighter Stephen Hunt got into difficulty inside the building at around 8.35pm, along with another firefighter, Greater Manchester Fire and Rescue Service said.
Both were pulled out by their colleagues and treated by the Ambulance Service before being taken to hospital.
More top news
Storm Imogen will cause problems across much of the south today, but it will be calmer in the north.
David Cameron is expected to warn that voting for a "Brexit" would result in refugee camps springing up across the south-east of England.
Beyonce, Coldplay and Bruno Mars performed a medley of their hits during a powerful half-time performance at Super Bowl 50.