Noah, who has not played since undergoing left knee surgery last month, tested positive for Selective Androgen Receptor Modulator LGD-4033, a substance intended to produce effects similar to those of anabolic steroids, the league announced.
Noah's ban will begin with the first NBA regular-season or playoff game for which he is eligible and physically able to play, which means he figures to miss the start of next season.
At 27-45, the Knicks are all-but eliminated from the playoff hunt, sharing 12th in the NBA's Eastern Conference and trailing Miami by eight games for the final playoff berth.
Noah tested positive for an over-the-counter supplement banned under the current league bargaining agreement with the players union, but under rules of the league-union deal starting in July, unintentional ingestion claims would be considered and a union statement said it did not think under those future terms Noah would have faced any punishment.
The National Basketball Players Association (NBPA) said neither Noah nor the union will appeal the suspension.
"After a thorough investigation, the NBPA believes that Joakim Noah did not intentionally or knowingly violate any policy," a union statement said.
"We believe that this isolated occurrence was a regrettable mistake. Joakim has offered his deepest apologies for this infraction."
The NBPA said Noah was "completely forthcoming and cooperative" throughout the investigation.
In 46 games this season for the Knicks, all of them as a starter, Noah has averaged 5.0 points, 8.8 rebounds and 2.2 assists.
The two-time NBA All-Star, who was named the league's 2014 Defensive Player of the Year, underwent arthroscopic knee surgery on February 4. He had also been nagged by a hamstring injury earlier this season.
Noah was not expected to return this season but depending on when he does, the punishment could see him forfeit between $2.5 and $2.75 million in salary.
Noah, 32, holds US, French and Swedish citizenship and first made his mark as a collegiate star at Florida, leading the Gators to consecutive US national tournament titles in 2006 and 2007.
After being selected ninth overall by the Chicago Bulls in the 2007 NBA Draft, Noah played for Chicago until last July, when he signed a four-year deal worth $72 million with the Knicks.