The 19-year-old forward participated in Lightning development camp this week.
The Tampa Tribune reported his recovery time will be 6-8 weeks, which leads up to the start of rookie camp Sept. 11.
Erne was the 33rd pick in the 2013 NHL Draft. He signed an entry-level contract April 1 and had a goal and three assists in eight games for the Syracuse Crunch in the American Hockey League.
Erne had 62 points (21 goals) in 48 games for the Quebec Remparts of the Quebec Major Junior Hockey League last season. He had 189 points (57 goals) in 180 QMJHL games over three seasons.
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