The Police Academy star passed away on Monday (15Feb16) in North Bend, Washington, aged 98.
One of his best known roles include the grouchy Henry Warnimont on 1980s sitcom Punky Brewster, who adopts the title character, played by Frye.
She paid tribute to her onscreen adopted dad by sharing a black and white image from the show on Instagram.com which shows Punky sat on Henry's shoulders.
In the caption, she writes, "When I reflect on some of the most joyous moments in my life, they were shared with this incredible man. The universe just gained a gigantic star. You will be in my heart and soul always & forever. Your little Punky RIP George Gaynes Love to your family."
Actress Olivia Munn also added a tribute on Twitter.com, writing, "Rest in peace #GeorgeGaynes #PunkyBrewster."