This page explains in detail the interactions between the Mario series and The Muppets series.
Muppets Babies episode It's Only Pretendo
September 15, 1990
Mario
The Muppets
Muppet Babies - Season 6 Episode 12 - It's Only Pretendo
The full episode. Mario references are at 00:07 and 3:48.
The first episode of season seven (eighty-fifth episode in total) of the Muppet Babies TV show is about the babies playing "Pretendo" games and imagine themselves as characters in them.
During the first part of the episode, Gonzo imagines himself in a Donkey Kong-like setting and imagines to be "Super Bario Weirdo", fighting a dragon named King Copacabana in place of Donkey Kong. While this is a reference to the Donkey Kong series, the hero's name is a reference to Mario being called Super Mario in his series, and the enemy being a dragon is a reference to Bowser, also considering that his name sounds like King Koopacabana.
Later, as Gonzo is searching trough his games, he names three of them as Super Bario Brothers, Son of Super Bario Brothers and Second Cousin of Super Bario Brothers. The first one is a reference to Super Mario Bros., and while the second one may be a reference to Donkey Kong Jr., the presence of so many "Bario Brothers" games is likely a reference to the Mario series being very popular at the time, and already featuring about 10 games.
License
Jim Henson Productions, that created Muppets Babies, held no right over Nintendo games, in fact they changed the name of the console to "Pretendo". The episode only features minor references to the Mario series.