Crosby is experiencing mild symptoms and is in the NHL COVID-19 protocol, Sullivan said. He missed practice on Wednesday because of the positive test.
Crosby, 34, had just returned to the Penguins' lineup Saturday after undergoing left wrist surgery on Sept. 8. He missed the team's first seven games, and the Penguins went 3-2-2 in his absence.
"I'm sure he's discouraged. He worked extremely hard to get to this point, and we were all so excited about getting him back in the fold," said Sullivan, via a Penguins statement. "This puts another roadblock in front of it. But we'll control what we can, and we're hopeful that Sid will return soon."
Players who test positive for COVID-19 are placed in isolation. Players can leave isolation after at least 10 days have passed since symptoms first appeared; at least 24 hours have passed since the last fever without the use of fever-reducing medications; and when team physicians conclude that the individual no longer presents a risk of infection to others.
The Penguins also announced that defenseman Brian Dumoulin missed practice after testing positive for COVID-19 but is asymptomatic. According to the NHL, asymptomatic players can return after two negative tests that are 24 hours apart.