The Blue Jackets (19-11-1), tied for first in the Metropolitan Division with the Washington Capitals, host the New York Islanders on Thursday (7 p.m. ET; FS-O, MSG+, NHL.TV). Center Jordan Schroeder was recalled from Cleveland of the American Hockey League and is expected to replace Dubinsky in the lineup.
Dubinsky centered Cam Atkinson and Boone Jenner last season and the three were reunited Tuesday in an effort to get them going offensively.
"It's certainly a loss," Tortorella said of Dubinsky. "It's an opportunity for someone else. We need to get better play, more consistent play out of a number of people."
Rookie Pierre-Luc Dubois centers the top line with Artemi Panarin and Josh Anderson. Centers Alex Wennberg, Lukas Sedlak and Schroeder will be asked to pick up minutes in Dubinsky's absence.
"You never want to see a guy get hurt like that, it's dangerous, but we have to make the most of it, and I have to make the most of it," Sedlak said.
Forwards Nick Foligno and Boone Jenner can also play center.
"It's next guy up," Foligno said. "We have to hold down the fort for [Dubinsky] and play well so we're in a good position when he comes back. We'll band together over this."
Dubinsky has 420 points (144 goals, 276 assists) in 731 games over 12 seasons with the New York Rangers and Blue Jackets.