The Hurricanes said Wednesday that they granted the All-Star forward the leave after his wife's sister, Tamara Stephenson, died of cancer at age 26.
"Our thoughts and prayers are with [wife] Tanya and Eric during this difficult time for their family," general manager Jim Rutherford said in a statement.
Staal, named to Canada's Olympic team last week, shares the Hurricanes' scoring lead with Ray Whitney with 27 points, and has a team-best 19 assists.
It is not clear when Staal will return to the team.
Information from The Associated Press was used in this report.