Damiao sidelined for six weeks
Damiao, who has scored 39 goals this season in all competitions, limped off during the first half of Wednesday's 1-1 draw with Figueirense in the Brazilian championship.
"Damiao suffered a grade two muscular injury," team doctor Paulo Rabello said on Inter's website.
"From the medical exam, we reckon that he can play football in 35 or 40 days' time. He has difficulty in walking."
The 22-year-old, who scored his first goal for Brazil this month in a 1-0 win friendly over Ghana, will miss Brazil's friendlies against Argentina, Costa Rica and Mexico as a result.