Neal saw the doctor Thursday and the Penguins announced the news Friday.
Neal, who has missed 21 games this season, has 22 goals and 49 points in 44 games.
"It won't be easy without him," left wing Jussi Jokinen told Triblive.com. "He is a great player. Everyone needs to chip in. It's been a tough year for him."
The Penguins start a home-and-home against the Philadelphia Flyers on Saturday (1 p.m. ET; NHLN-US) at Wells Fargo Center.
Forward Chris Kunitz (leg) practiced Friday after not doing so Thursday. His status for the weekend is not determined.
Kunitz collided with the goal post in a 2-0 win against the Washington Capitals on Tuesday.