The Italian team did not disclose a timetable for Gallinari's recovery but said he would miss next month's EuroBasket tournament.
Gallinari grabbed his knee after a bounce pass in the lane while playing against Georgia in Brescia, Italy. He hobbled over to the sideline, holding the back of the knee as trainers rushed to his aid, before limping to the locker room with the help of a staff member and a teammate.
"It's tough to talk about basketball after what what we saw happen to Danilo," Italy captain Luigi Datome said after the team's 91-84 win. "We wish him, of course, the best."
Gallinari, 34, signed with the Celtics on July 12 via the midlevel exception and was counted on for depth as Boston looks to return to the NBA Finals.
A first-round draft pick of the New York Knicks in 2008, Gallinari has averaged 15.6 points and 4.7 rebounds per game in his career while also playing for the Denver Nuggets, LA Clippers, Oklahoma City Thunder and Atlanta Hawks.