The British trio performed a cover of Nirvana's 1991 track Lithium during a headlining set on Saturday night (05Apr14).
Introducing the tune in Sao Paulo, frontman Matt Bellamy said, "Someone great died 20 years ago - this next song is for Kurt Cobain."
Cobain was actually found dead in his Washington home on 8 April, 1994, but medics ruled he had committed suicide three days before his body was discovered.
Muse's performance at Lollapalooza Brazil came just days after the band was forced to scrap another Sao Paulo show at the Grand Metropole on Thursday (03Apr14) after Bellamy lost his voice in rehearsals.
Meanwhile, the trio wasn't the only act remembering Cobain this weekend - St. Vincent performed Lithium during her concert in Chicago, Illinois on Friday night (04Apr14).