Hill's ban began Friday night when the Islanders faced the Buffalo Sabres in Game 5 of the first-round Eastern Conference playoff series. The earliest Hill could return to the lineup would be the Stanley Cup final.
Islanders' spokesman Chris Botta said Hill did not travel with the team to the arena for Friday night's game. He said he did not know whether Hill had travelled back to Long Island.
The nature of Hill's infraction was not immediately clear. An NHL spokesman said the league was obliged to honour the player's confidentiality and would not comment.
New York started the day in a 3-1 hole to top-seeded Buffalo in the best-of-seven matchup.
Hill, 37, had one goal and 24 assists in 81 games this season, his first with the Islanders.
He did not record a point in the Islanders' first four playoff games against Buffalo.
As part of the new collective bargaining agreement that ended the yearlong lockout in 2005, a player receives a 20-game suspension for a first positive test and is subject to a mandatory referral to the league's substance abuse-behavioural health program for evaluation, education and possible treatment.
Every NHL player can be given up to two "no-notice" tests every year, with at least one conducted on a team-wide basis. Players can be given a "no-notice" test at any time.
It's the first 20-game suspension handed out under the policy.
Defenceman Bryan Berard of the Columbus Blue Jackets and Colorado Avalanche goalie Jose Theodore both failed out-of-competition tests administered by their respective national anti-doping organizations.
But neither was suspended by the league because the failed tests happened before the NHL established its new policy.
Berard's urine test on Nov. 12 showed traces of the steroid 19-norandrosterone.
He was banned from international competition for two years. He was tested by the U.S. Anti-Doping Agency because he was on the U.S. Olympic hockey preliminary roster released last September.
Theodore, who was on Canada's preliminary 81-man Olympic eligibility list but not named to the final squad, failed a doping test Dec. 9.
The urine sample showed Finasteride, a masking agent for steroids that is also commonly found in hair-restoration drugs.
The NHL's anti-doping policy has been called into question by Dick Pound, chairman of the World Anti-Doping Agency.
He said last year that the policy was "very seriously flawed" and made headlines in November 2005 when he estimated that one third of NHL players were likely taking performance enhancing substances - mainly stimulants.
The NHL does not test for the drugs on WADA's list of banned substances that are prohibited only during competition, such as stimulants. Some cold remedies that contain stimulants, such as ephedrine, are suspected to be widely used by hockey players.
Players as well as league and union officials unanimously denied Pound's claims.
Hill, a native of Duluth, Minn., was drafted by the Montreal Canadiens in the eighth round of the 1988 NHL entry draft. In 841 career regular-season games, Hill has recorded 60 goals and 229 assists for 289 points.