General manager Jim Rutherford said Monday that Bennett has symptoms and the team is awaiting test results before making a diagnosis. Penguins captain Sidney Crosby is out for Monday night's game against Tampa Bay after being diagnosed over the weekend.
Rutherford said Crosby is past the infectious stage and could return to the team as early as Tuesday.
"He probably could have been here today, but we took an extra day to be cautious, and as far as I know he will return tomorrow or the next day," Rutherford said.
The Penguins are one of a handful of NHL teams dealing with a mumps outbreak. The virus usually is found in children, and its symptoms include facial swelling and fatigue.
"We've taken the proper steps to make sure that he is quarantined and not around anybody else at this point in time," Rutherford said of Bennett.
The 23-year-old Bennett has struggled to stay healthy during his brief career. He is already out indefinitely while recovering from a lower body injury against Boston last month. Bennett attended a function at Pittsburgh's Children's Hospital last week with the team.
The hospital said in a statement Monday that children who have not received an age appropriate vaccine will be put in isolation and monitored for symptoms.
"They're testing any possible people he may have come in contact with and they're on top of the situation," Rutherford said. "We feel bad about that. At that point in time, obviously he is not tested to be positive."