Ter Stegen missed Barca's recent games after being ruled out of Germany's friendlies following an injury sustained while training with his country during last month's international break.
"After intensive conversations with the medical team of the Club and various supporting experts, we decided to undergo a surgical procedure," Ter Stegen wrote on his Instagram account.
"The break obviously annoys me. It is the right and safe decision in order to come back in the best conditions for my Club @fcbarcelona and National Team @dfb_team."
Barcelona put no timescale on his return, but local media reports said Ter Stegen would be out for several weeks and could miss the Champions League knockout stages in February.
The former Borussia Monchengladbach player has made 17 appearances for the Catalan side this season, keeping eight clean sheets.
He received the Zamora Trophy last season as the best goalkeeper in LaLiga - conceding 18 goals in 37 games and helping Barca to their first league title since 2019.