Pato was carried off injured in the 70th minute of the goalless draw against Udinese after falling awkwardly in a challenge with defender Christian Zapata.
He will be in plaster for at least a month, Milan club doctor Maurizio Gevi said.
"He will then have to have rehabilitation," Gevi told reporters. "He won't be going to the Copa America. His season is over."
After an injury-plagued 2010, 21-year-old Pato had returned to top form for his club this year, scoring a number of crucial goals to help Milan win the Serie A title for the first time in seven years.
‘I was close, very close, to managing Liverpool. I thought it was done, but they went for Joe Fagan. From there, nothing worked out and I lost my motivation’: Ex-Real Madrid boss reveals missing out on Anfield job
‘When I proposed to my wife, I made it a condition that she learn the words of Good Old Arsenal, released before when we won the Double. She did it, too’: Arsenal legend stipulation he made his partner over famous 1971 Gunners song
