Grover spoofs John Travolta's famous Saturday Night Fever pose on the cover of the 1978 LP Sesame Street Fever.
Kermit dressed as Travolta, with Miss Piggy as Olivia Newton-John, in a spoof in The Miss Piggy Calendar 1982, "Saturday Night Greaser". (The title is a spoof of two popular Travolta films, Grease and Saturday Night Fever.)
A poster of Travolta can be seen on the wall of a boy's bedroom in episode 503 of The Muppet Show.
Travolta contributed a "Lobster with Three Sauces" recipe for Miss Piggy's 1996 cookbook, In the Kitchen with Miss Piggy.