The man, a French tourist, was stretchered into a waiting ambulance just after 3pm.
Police officers earlier held up a tarpaulin to block the view.
A large number of members of the public had gathered to watch the man's rescue.
A family of Belgian tourists were on the scenic tram ride through the city when they heard a "loud crack".
The tram driver and others rushed to help the man.
A large group of people tried to lift the huge branch off the man but it was too heavy.
Firefighters were soon on the scene.
One of the Belgian tourists was able to communicate with the man in French. He's gone to the hospital with him.
"We hope he is ok. It is very scary," one of the tourists said.
Some onlookers say that others had a near miss as the branch crashed down.
A Christchurch City Council spokeswoman confirmed the tree comes under its jurisdiction. She said arborists are currently examining all trees in the area.
Rolleston Ave has been reopened to traffic.
A Christchurch Transport Operations Centre (CTOC) spokesman said: "It is still very windy with a strong nor-westerly wind blowing through the city. We ask the road users take extra care."
The area is busy this afternoon with tourists and families as temperatures soar above 30C.
It is believed the man was injured when a large branch snapped off in the blustery warm nor'west winds beside the Canterbury Museum and Botanic Gardens.
The incident comes after five people were injured when a tree fell at the Shotover Jet base in Queenstown yesterday.
Two preschool children were among a family from overseas who were injured by a falling tree on the riverbank at Arthurs Point Rd.
A mother and son remain in Dunedin Hospital after the incident at about 1pm yesterday.
The pair, from Wellington, are both in a serious but stable condition.
Police are continuing to make enquiries into this incident.
Police said they were called to Rolleston Ave today following a report of a fallen tree branch.
"One person was initially trapped - I understand they were freed by fire, and are being looked at by ambulance," a spokeswoman said.
