The injury occurred in last week’s quarter-final against Suwon Bluewings in Qatar which went to a penalty shootout before the Japanese side progressed.
Iniesta was absent when Vissel lost 2-1 to another South Korean side, Ulsan Hyundai Motors, in the semi-final on Sunday.
“After many tests I took the advice of my medical team and we have considered that the best option for me was to get surgery and speed up the recovery.
Iniesta joined Kobe in 2018 after making 442 appearances for Barcelona, where he was the midfield dynamo in some of the club’s greatest ever teams.
Iniesta was a key part of the Barcelona sides that won trebles in 2009 and 2015. In all he won nine La Liga crowns and four European Champions League titles and orchestrated Spain’s 2010 World Cup triumph in South Africa.