The actor, best known for his role on soap opera EastEnders, is said to have undergone reconstructive work on his skull after his Mini Cooper car smashed into a steel barrier in Derby, England, on Wednesday night.
Gaffney is recovering at the Royal Derby Hospital but his condition is said to be "not life-threatening".
A source tells The Sun newspaper: "The airbags went off but Dean got a serious smash on his head. He passed out and there was a lot of blood. The car was so folded up he had to be cut out by firefighters."
Gaffney had been driving home after performing in a stage production of Agatha Christie's A Murder Is Announced at the Derby Theatre.
Theatre manager Gary Johnson says: "It is really sad news. We were all shocked when we found out and it seems to have been a really nasty accident. It must have happened when he was on his way home. All our thoughts are with him and we wish him a speedy recovery."
The show's remaining performances are to go ahead as scheduled.