The Robbie Jackson actor, who has also appeared in I'm a Celebrity, was travelling home from a performance of Agatha Christie thriller A Murder Is Announced when the incident occurred.
Gaffney was originally thought to be "fighting for his life" after a tweet from actor Tamer Hassan asked fans to "pray for" the 34-year-old, and it has been reported that he suffered serious head injuries.
However, Gaffney's manager Dave Read told The Mirror that the star is "being looked after" in a Derby hospital and "going to be okay".
"I haven't spoken to Dean myself but I'm hearing from family members that he is going to be alright - he's very lucky," Read said.
"It was very bad - he's lucky to be with us."
Dane Bowers, Kenzie and Rhian Sugden are among those who have sent Gaffney well-wishes on Twitter.