General manager Doug Wilson said Tuesday that Couture had the operation last week and is expected to be fully recovered by the start of training camp.
Couture hurt his hand fighting with Los Angeles' Mike Richards in Game 6 of a first-round series.
The Sharks became the fourth team in NHL history to lose a best-of-seven series after winning the first three games.
Couture had 23 goals and 31 assists in 65 games last season.
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