The Australian No.3, playing his first match of the European clay-court swing, defeated the local wildcard 6-4 6-3 in 82 minutes.
Italian Musetti will be a much tougher prospect. The 21-year-old beat Novak Djokovic in Monaco last week for the biggest result of his career.
Earlier Casper Ruud extracted revenge for an embarrassing defeat as he reached the last 16.
The third-seeded Norwegian lost to Ben Shelton last year in Cincinnati, where the American was a relatively unknown college player ranked 229th in the world. But on Tuesday on clay he won 6-2 7-6 (7-1).
"I wanted my revenge," Ruud said. "Different surface, different continent, different tournament . . . I felt like I had a little bit more time here to build the points on clay, which is normal."
Defending champion Carlos Alcaraz opened with a comfortable 6-3, 6-1 win over Portuguese Nuno Borges.
The top-seeded Spaniard, No. 2 in the world, converted five of his seven break opportunities to secure victory.
"It's always different to play here, it's not just any other tournament for me," the 19-year-old said. "I'm at home, with the fans behind me. It's always nice and special."
Alcaraz's next opponent will be fellow Spaniard Roberto Bautista Agut, the 13th-seed who defeated Bernabe Zapata Miralles 6-2 6-2.
Fifth-seeded American Frances Tiafoe lost 6-4, 6-7 (3-7), 6-4 to Emil Ruusuvuori of Finland. The 40th-ranked Ruusuvuori rallied from 3-0 down in the final set.
In other ties Diego Schwartzman defeated Wu Yibing to set up second-round tie with fourth-seeded Jannik Sinner, David Goffin beat Feliciano Lopez and Alejandro Davidovich Fokina knocked out Tomas Martin Etcheverry.
In Munich's ATP250 event Australia's Chris O'Connell, who grabbed a slot after Briton Jack Draper pulled out, won his opening match against France's Ugo Humbert 6-4 6-4. He now plays No.3 seed Alexander Zverev, who received a first-round bye.
Other players moving into the last 16 included Dominic Thiem, Marton Fuscovics and Oscar Otte, who knocked out No.5 seed Sebastian Baez 6-3 7-5.
O'Connell and Kubler are among seven Australians named on Tuesday in the main draw for the French Open. Alex de Minaur and Nick Kyrgios head the contingent with Alexei Popyrin, Max Purcell and Jordan Thompson also headed for Paris.
- with agencies
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