Auger-Aliassime already has one singles title to his name this year, having prevailed in Rotterdam, and also reached the final of the Open 13 in Marseille and helped Canada to victory in the ATP Cup at the start of 2022.
However, the sixth seed entered this contest with just one win from his last four matches and came unstuck once again at the hands of Musetti.
Musetti, who won two sets in the fourth round of the French Open against Novak Djokovic last year, is very much at home on the clay in Monaco.
He demonstrated that in 6-2 7-6 (7-2) success, setting up a last-16 meeting with Diego Schwartzman.
“I live here and practice here,” Musetti said in his on-court interview. "It is nice to be here and play here in front of such a crowd. I am really happy.
"My backhand down the line was a key to many of my great shots. After a really good first set, he came back with such powerful serving, but I was calm and patient and that was the most beautiful thing about today."
Auger-Aliassime's exit came a day after top seed Djokovic was knocked out in the second round by Alejandro Davidovich Fokina, but there were no such problems for second seed Alexander Zverev as he saw off Federico Delbonis in straight sets.
Fifth seed Andrey Rublev came from a set down to defeat Alex de Minaur and fourth seed Casper Ruud, coming off his defeat in the final in Miami, edged qualifier Holger Rune in two tight sets.
The man who vanquished Ruud in Florida will go no further on the Cote d'Azur, however, Carlos Alcaraz losing in just over three hours to Sebastian Korda on his Monte Carlo debut.
Korda lost to Alcaraz in the final of last year's Next Gen ATP Finals, but avenged that defeat with a 7-6 (7-2) 6-7 (5-7) 6-3 victory.
World number 10 Cameron Norrie lost to Albert-Ramos Vinolas and his British compatriot Dan Evans fell to David Goffin, while 16th seed Lorenzo Sonego was beaten by the in-form Laslo Djere.
Elsewhere in the draw, there were wins for Jannik Sinner, Taylor Fritz, Hubert Hurkacz and Pablo Carreno Busta.