The NHL named Crosby the first star for the month after the Penguins captain's 25 points in 15 games helped Pittsburgh go undefeated in March.
Montreal defenceman P.K. Subban was named second star, while Columbus goaltender Sergei Bobrovsky took third-star honours.
In weekly award winners, Toronto forward Joffrey Lupul was named first star, followed by San Jose goaltender Antti Niemi and Edmonton forward Taylor Hall.
Crosby is out indefinitely with a broken jaw after he was hit in the mouth with a puck in the first period of Pittsburgh's 2-0 win over the New York Islanders on Saturday.
Prior to that, the NHL's leading scorer had a stellar month with six goals and 19 assists as Pittsburgh went 15-0-0 for March. He also tied linemate Pascal Dupuis for a league-leading plus-19 rating.
He also matched a career high with five assists against the Islanders on March 10, becoming the only active player with more than one five-assist game in his career
The 25-year-old Cole Harbour, N.S., native leads the NHL with 41 assists and 56 points in 36 games this season. He also ranks second in the league with a plus-26 rating and 14 power-play assists.
Subban led all defencemen in March with 18 points (seven goals, 11 assists) in 14 games, including a league-leading 11 power-play points.
The 23-year-old Toronto native leads all NHL defenceman this season with 10 goals and ranks third with 27 points in 28 games.
Bobrovsky led the NHL with three shutouts and also ranked second in wins (nine), goals-against average (1.49) and save percentage (.950) as Columbus went 10-2-4 in its most successful month in franchise history.
The 24-year-old Russian is 12-8-6 in 26 games this season, ranking second in the league with a .927 save percentage and eighth with a 2.13 goals-against average.
Lupul had a league-high nine points (five goals, four assists) in four games last week, including three game-winning goals.
Niemi led goaltenders last week with four wins — two of them shutouts — while putting up a 1.22 GAA and .952 save percentage.
Hall had five goals and eight points in four games with Edmonton. He broke Wayne Gretzky's franchise record for the fastest hat trick to start a game when he scored three times in the first 7:53 of Saturday's 4-0 win over Vancouver.
Meanwhile, Los Angeles defenceman Jake Muzzin was named the rookie of the month after recording four goals, seven assists and a plus-10 rating in 17 games. Chicago left wing-Brandon Saad, Florida centre Jonathan Huberdeau, Montreal right-wing Brendan Gallagher, St. Louis goaltender Jake Allen and Ottawa goaltender Robin Lehner were also considered.