Sutter, 22, will make $1.5 million in 2011-12, $2 million in 2012-13 and $2.7 million in 2013-14, the Hurricanes said in a statement.
"Brandon is one of the cornerstones of our franchise moving forward," said General Manager Jim Rutherford.
"He is an extremely intelligent player who can perform in all situations, and has already grown into a leadership position for the Hurricanes at a very young age."
Sutter, who was Carolina's first-round selection in the 2007 NHL Entry Draft, had 14 goals and 15 assists in 82 games for Carolina last season and led the team with a plus-13 rating.
In three seasons with Carolina, Sutter has 36 goals and 39 assists in 204 games.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Frank Pingue)