Botman suffered the injury in Saturday's 2-0 FA Cup quarter-final defeat by Manchester City that ended Newcastle's hopes of silverware this season. He will also now miss the Netherlands' campaign at Euro 2024.
"Sven Botman will undergo surgery next week after suffering a knee injury against Manchester City," Newcastle said in a statement.
"A scan has confirmed that he sustained an injury to his ACL and he is expected to return within six to nine months.
"We wish you a full and speedy recovery, Sven."
Injuries to key players have been a major factor in a disappointing season for Newcastle.
Backed by the Saudi sovereign wealth fund, they finished fourth in the Premier League last season to reach the Champions League for the first time in 20 years.
But the Magpies crashed out of Europe in the group stage, sit 10th in the Premier League and have failed to end their wait for a first major trophy since 1969 in the domestic cups.
