Motta suffered a hamstring injury just four minutes after his introduction as a substitute in Sunday's Euro 2012 final between Italy and Spain.
The midfielder was stretchered off and looked in some pain, leaving Italy down to 10 men having made all three changes and exposed to a ruthless Spain side who were winning 2-0 at the time and went on to register a 4-0 triumph.
Motta's preparations for the new Ligue 1 season will now be disrupted by his recovery from the injury.
"It was a dangerous injury behind the thigh," Ancelotti said.
"It's dangerous but that's normal. I think he cannot train for at least a month."
Motta will not return to his club until late July, along with PSG goalkeeper Salvatore Sirigu, who was also a member of Italy's Euro 2012 squad.