The 29-year-old had surgery in New York on Friday, which the Nets deemed successful.
"Lin will miss the remainder of the 2017-18 season, but is expected to make a full recovery," the team said on its website.
On Twitter, Lin posted a picture of himself in hospital, wearing his surgical gown.
"THANKS for all the love and support!! Blown away at everyone's kindness," he wrote.
Lin's absence is a bitter blow to the Nets, who already had been predicted to be one of the league's cellar dwellers.
The first American of Chinese or Taiwanese descent to play in the NBA, Lin was born in northern California to parents who had emigrated from Taiwan.
He went from an obscure professional basketball player to an overnight sporting sensation in 2012 when he led a winning turnaround for his former New York Knicks team.
He averaged 20.9 points and 8.4 assists per game in February of that year while leading the Knicks to 10 wins in a 13-game stretch that overwhelmed New York City and caught the imagination of Knicks fans.
Lin went on to appear on the covers of numerous magazines, and replicas of his No. 17 jersey soon became a top seller amid a media and fan frenzy around him nicknamed “Linsanity”.
He went on to play for the Houston Rockets, Los Angeles Lakers and Charlotte Hornets before signing a three-year, $36 million contract with Brooklyn last year.
Lin was the second big-name NBA player to suffer a likely season-ending injury in his team's opening game of the season.
On Tuesday, Boston's newly-acquired All-Star forward Gordon Hayward suffered a dislocated left ankle and fractured tibia in a collision under the basket with LeBron James of the Cleveland Cavaliers.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Rex Gowar)
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