The crane, on hire from HTC Plant, fell backwards onto a four-storey apartment building on Tabley Street at lunchtime.
A spokesperson for Merseyside Fire and Rescue Service said the crane operator has been taken to hospital, and was conscious at the time.
The spokesperson said rescue crews had carried out a full door-to-door search of the building as they had received calls from residents trapped in their homes due to damage to escape routes. Eight adults were rescued from the third and fourth floors of the building, with no injuries.
