He replaces centre Mike Fisher, who is out indefinitely with a left knee injury.
Hennessy made his NHL debut Dec. 12 in the Senators' 3-2 win over the Red Wings in Detroit. In two games, he recorded one shot on goal and averaged 6:33 of ice time. He was returned to Binghamton on Dec. 15.
The 21-year-old native of Brockton, Mass., is third in scoring in Binghamton with 26 points (12-14) in 32 games.