Police found the 60-year-old Gellar in bed at his home after being called to the scene by a friend who had reported Gellar missing for several days. Investigators suspect drugs may have played a part in his death since medication was discovered near his body.
An unnamed family friend tells the Daily News that Arthur was reportedly going through cancer treatment and was also "suffering from depression."
So far Gellar has remained mum on the death, with both the 24-year-old Buffy the Vampire Slayer star and her reps declining to comment on the news.
But Gellar has made it clear in the past she had no love for the man.
"He is not a person who exists in my life," Sarah once told TV Guide. "Just because you donate sperm does not make you a father. I don't have a father. I would never give him the credit to acknowledge him as my father."
Gellar never divulged the reasons for the rift with her dad, but divorce from her mother, Rosellen, may have had something to do with it. Gellar's parents split up when she was 8 and the actress was raised by her mom.
For his part, Arthur Gellar told the Scottish Daily Record in December that he thought he and his famous daughter might one day patch things up
"There isn't a night that goes by that I don't think of her."
The New York City medical examiner's office is scheduled to perform an autopsy today to determine the cause of death.
As for the younger Gellar, there's at least some good news on the horizon. The teen icon, whose character was brought back to life at the start of Buffy's sixth season (which last week debuted to big ratings on its new home, UPN), is planning to tie the knot with longtime beau Freddie Prinze Jr. later this year. The two are also costarring together as Fred and Daphne respectively in the upcoming big-screen version of Scooby-Doo.