Doughty left midway through the first period of a 2-1 loss against the San Jose Sharks on Thursday after delivering a hit on forward Tyler Kennedy and did not return.
Doughty did not take part in a brief optional practice here Friday afternoon and had his left shoulder wrapped in ice in the locker room.
"He might play tomorrow," Sutter said.
Doughty leads Los Angeles in ice time at 25:42 per game and is fifth in scoring with 27 points.
Los Angeles has clinched a berth in the Stanley Cup Playoffs and will finish third in the Pacific Division.
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