Campaigner and Unite member George Tapp, 64, was injured when a car was stopped by protesters outside BAM’s £100m Manchester City Training Academy site.
Tapp also suffered a fractured kneecap and was treated at Manchester Royal Infirmary.
Police spokesman Chief Superintendent Russ Jackson from North Manchester division said: “From what we can see from CCTV, protesters were blocking Ashton New Road, preventing motorists from going any further.
“A number of people stood in front of the Ford Ka and climbed upon the bonnet before it moved forward.
“The car then travelled a short distance at a slow speed before it stopped and one of the men fell off. The car reversed and drove off.
“We are working to ascertain whether any criminal offence has occurred and I would ask the driver of the car or anyone who witnessed the incident to contact police.
“Officers are now in the process of talking to representatives of Unite Union and BAM Construction to establish what happened last night.
“While we respect the democratic right of anyone holding a peaceful protest, if we believe individuals have behaved in an unlawful manner, we will take action.”