Malkin has symptoms that include a severe headache and mild disorientation, the newspaper reported, citing multiple sources.
Penguins coach Dan Bylsma said a concussion has not been ruled out, but disputed that Malkin suffered from headaches and disorientation.
Malkin was injured in the third period of Friday's game against the Panthers after getting nudged by Florida's Erik Gudbranson. Malkin's back hit the boards at full speed and his head snapped back upon impact.
Bylsma ruled Malkin out for Sunday's game against Tampa Bay. Bylsma declined to elaborate on the nature of what is being called an "upper body" injury but added that Malkin is not hospitalized.
"It's hard to know what to expect in any situation of this nature," Bylsma said.
Bylsma said the club was following "NHL protocols" and will monitor how Malkin recovers before giving any sort of timetable on when he might return.
Pittsburgh's second-leading scorer, Malkin has registered 14 goals and 25 points in 22 games this season. The Russian center collected 50 goals and 109 points last season en route to winning the Hart Trophy.
Information from The Associated Press was used in this report.