San Jose Sharks winger Ryane Clowe was also named the rookie of the month on Tuesday.
Heatley led all NHL scorers in January with 22 points (11 goals, 11 assists) in 13 games, and posted a League-best plus-14 rating.
The Senators went 9-3-1 and improved to second place in the Northeast Division. Heatley had seven multiple-point games, including a four-point night in a win over Buffalo on Jan. 3.
Crosby was named the second star after scoring 21 points (eight goals, 13 assists) in 12 games. The league's top point-getter had at least one point in all but one game last month.
Luongo was given the third star after posting an 8-1-2 record with a 1.86 goals-against average and .945 save percentage.
Clowe was named the league's top rookie in January after putting up 16 points (nine goals, seven assists) and a plus-10 rating in 11 games.
The native of Fermeuse, N.L., edged Pittsburgh's Evgeni Malkin, Colorado's Paul Stastny and Anze Kopitar of the Los Angeles Kings.