Scolari, who was best known for his role opposite Tom Hanks in the 1980s cross-dressing sitcom "Bosom Buddies", died after a two-year battle with cancer, aged 66.
The actor scored an Emmy in 2016 for playing Lena's dad on "Girls" and she was quick to comment on the sad news on Friday, writing, "I couldn't have been raised up by a better TV papa."
In a heartfelt Instagram post, alongside a snap of herself and Scolari from "Girls", she shared, "The shyest extrovert, the most dramatic comedian, the most humble icon. You had lived enough life to know that a TV show was just a TV show, but also to appreciate just what it meant to be allowed to play pretend for a living - and you never let us forget that this job was a privilege..."
"When we told you that (your character) would be coming out of the closet on the show you said 'thank.. you, you can trust me with this.' Becky Ann Baker and I loved every second of playing your family and I couldn't have been raised up by a better TV 'papa.' Thank you, Scolari, for every chat between set ups, every hug onscreen and off and every 'Oh, Jeez.' We will miss you so much."
Scolari also received three Emmy nominations for his role as Bob Newhart's boss on 1980s sitcom "Newhart".
"I knew that Peter was sick, but his death still comes as a great shock," 92-year-old Newhart wrote in a statement to Variety on Friday.
"We were friends and colleagues for over 40 years. Julia (Duffy) and Peter, as a vacuous couple (Michael and Stephanie), were an essential part of the success of 'Newhart.' In life, he was a fantastic person, and it was a joy to work together. He will be sorely missed and his passing at 66 is much too early."
Duffy also remembered her former "Newhart" co-star, writing "No better partner," alongside a photo of the two doing the tango in an episode of the sitcom.
"There wasn't a sweeter man on the planet. We performed together in 'Hairspray' for a time and he was always a total delight. Farewell, dear Peter," Harvey Fierstein tweeted.
And Michael McKean, who co-starred with Scolari in the Off-Broadway play "The True", wrote on Twitter, "We knew this was coming. Doesn't make it easier. RIP, Peter my friend."