He made 25 Eredivisie appearances in 2023/24 and scored twice as PSV won their first Dutch league title in six years, but suffered an ACL tear in April that ended his season.
The injury required surgery and ruled Dest out of the US squad for Copa America.
"Sergino is rehabilitating and will not join group training for the next few months," PSV said in a statement.
Dest said he felt greatly appreciated at PSV.
"The club is incredibly warm, like I've never experienced anywhere before. Those are important aspects for someone in my situation and give me confidence that I can rehabilitate well here," he said.