"We're going to hold him out for this week," Sullivan said, according to the team's website. "He's going to work with our medical and training staff for this week. We'll evaluate him as we go.
"We think it's in the best interest of 'Geno' and the team to take this approach, as far as getting him into a position to be ready to help this team."
Malkin ranks among the league leaders with 23 goals and 49 points.
Sullivan didn't want to describe Malkin's injury as a "long-term" concern, but he also said, "I don't want to sit here and say it's day-to-day."
The coach said the Penguins, however, would not rush Malkin back and risk making the injury worse.
"We obviously want him in our lineup. But we're also concerned that we do the right thing for our athletes and our team long-term. We're making sure we take a cautious approach," he said, according to the team's website.
Malkin will stay behind during the team's road trip to work with the training staff. The next chance for Malkin to play will be on Feb. 18 against Detroit.
Information from The Associated Press was used in this report.