Djokovic, a two-time winner in the Principality in 2013 and 2015, was broken eight times before going down 4-6, 7-5, 6-4 on a wet and chilly day on the Cote d'Azur.
"(The) feeling is terrible after playing like this, honestly. But congrats to him. He stayed tough in important moments, and that's it," said Djokovic.
The Serb led by a set and a break against Musetti, but the Italian youngster fought back in a scrappy second set and then prevailed in the decider after rain interrupted the match for an hour.
Musetti, ranked 21st, advances to a quarter-final meeting with compatriot Jannik Sinner, who saved a match point before beating Poland's Hubert Hurkacz 3-6, 7-6 (8/6), 6-1.
Djokovic, the big favourite in the absence of Rafael Nadal and Carlos Alcaraz, surged 5-2 ahead in the opening set. He dropped serve as he tried to close it out before breaking Musetti for a third time.
The top seed again looked in control at 4-2 in the second but was broken to love in a game that started with Djokovic justifiably unhappy over a line call that went against him.
Musetti won the next three games, successfully serving for the second set at the second attempt after blowing his chance while leading 5-4.
A rain shower early in the deciding set forced play to be suspended, with Musetti landing the decisive break to go 5-3 up and eventually sealing victory on his fourth match point.
Djokovic has not gone beyond the last eight in Monte Carlo since 2015.
"I don't think it's catastrophic, but my feeling is bad right now because I lost the match. That's all," said Djokovic.
"It's not a great day for me, so I'm not really in the mood to speak."
Ruud awakening
French Open finalist Casper Ruud also bowed out after suffering a 6-1, 7-6 (8/6) defeat to German Jan-Lennard Struff, who has beaten the Norwegian on all three occasions they have met.
The 100th-ranked Struff -- who came through the qualifiers -- will play Andrey Rublev in the quarter-finals after the Russian beat his compatriot Karen Khachanov 7-6 (7/4), 6-2.
Ruud was on a run of nine successive victories on clay -- having won in Gstaad last July and then Estoril on Sunday -- but he looked out of sorts in Monaco.
The world number four, who also reached the US Open final last year, saved two match points and fought back from 5-2 down to lead 6-5 in the second set only for Struff to level.
The German then took a hard-fought tie break when Ruud sent a return out.
Matteo Berrettini withdrew due to a muscular problem the Italian suffered in Wednesday's three-set marathon win over Francisco Cerundolo.
Berrettini's withdrawal allowed Denmark's ninth-ranked Holger Rune to move into the last eight of the tournament for the first time.
The 19-year-old will face the winner of the match between in-form Russian Daniil Medvedev and Germany's Alexander Zverev, who is still battling back to form after a long injury absence.
Two-time defending champion Stefanos Tsitsipas breezed through his third-round match, the Greek swatting aside Chile's Nicolas Jarry 6-3, 6-4.
Tsitsipas goes on to face Taylor Fritz after the American eighth seed defeated Jiri Lehecka of the Czech Republic in three sets.
