The actor was crossing the street in Hollywood when he was struck in the head by the side mirror of an SUV. The motorist who hit Woolf stayed at the scene and was not cited or arrested.
Woolf was rushed to a local hospital and was listed in critical condition Friday.
"We have been overwhelmed by the outpouring of love and support from all over the world for our beloved Ben," his family said in a statement. "He touched so many hearts in his 34 years. His memory will live on within each of us and within his work."
Woolf's publicist Zack Teperman also released a statement.
"Ben was one-of-a-kind and will never be forgotten. The time we all shared together will be remembered forever," the statement said.
PHOTOS: Celebrity deaths in 2015