The team announced the decision on Sunday. Bargnani will miss at least the first three games against Chicago, Cleveland and Charlotte. After those three, the Knicks face Washington on Nov. 4.
Bargnani hasn't played since Oct. 8 when he played 19 minutes and had eight points in the preseason opener against Boston.
"I wouldn't necessarily like to put him in that position where without some quality practice time, put him into a game situation," coach Derek Fisher said. "That's why hamstrings are problematic, because one day you're feeling better, but all it takes is a little bit of a tug and it sets you back."
"It's about trying to make sure he's healthy before he goes out and it's not something that he has to kind of question once he's out on the court," Fisher added.
Point guard Jose Calderon (calf) said he is optimistic about being ready for Wednesday's opener against the Bulls.
"That was the plan from the beginning," said Calderon, who sat out the last two preseason games. "Hopefully everything goes as planned and I will be ready for Wednesday."
The Knicks had an open practice at Madison Square Garden on Sunday. Veteran forward Travis Outlaw was not with the team on the court. The team could trade or waive Outlaw soon, as reported by ESPNNewYork.com on Saturday.
Outlaw is owed $3 million this season.