The pet's ailing health also is forcing Tortorella to miss the NHL's All-Star Weekend in Los Angeles, where he had been selected to serve as a coach for the Eastern Conference's Metropolitan Division.
The sick dog is a 10-year-old pit bull, Emma, who belongs to his son, Nick, who is a U.S. Army Ranger stationed abroad.
Tortorella's affinity for animals -- especially pit bulls -- is well known. His family's foundation -- The John and Christine Tortorella Foundation -- has promoted animal rights and found homes for several rescue and foster dogs.
"I needed to see this through," Tortorella told The Columbus Dispatch, one day after announcing his absence would be due to a personal matter.
"I appreciate so much the number of messages I have received since the announcement," Tortorella said. "But this absolutely is not an emergency. I want to clear that up."
Blue Jackets captain Nick Foligno said the players understood Tortorella's reasoning for the absence.
Tortella added: "I needed a few days during the All-Star break -- not having to go to the All-Star Game -- to take care of something very important to my family and my son."
Tortorella would have missed Thursday's game regardless, due to the NHL's All-Star Game attendance rule.
The Blue Jackets have a 32-12-4 record, earning Tortorella a spot behind the bench for Sunday's All-Star Game tournament.
Tortorella also coached the United States in the World Cup of Hockey.