Marx, 29, was forced to leave the Springboks' World Cup-winning squad after only one game in France following an injury to his knee during training.
Defending Japan Rugby League One champions Kubota said he would not be in their squad for the new season, which kicks off in December, but he was scheduled to return before his contract expires in May 2025.
"Unfortunately, due to my injury I won't be able to play next season but I will be back for the following season, hopefully," Marx said in a video message.
"Please carry on your amazing support towards the team. I think the team and everybody really appreciate it."
Marx was forced out of the World Cup when he went down in training after "having his knee caught in contact" before the Springboks' pool stage game against Romania.
Head coach Jacques Nienaber opted against calling up a direct replacement, with back-rowers Deon Fourie and Marco van Staden offering cover in the No. 2 shirt, as well as Bongi Mbonambi.
Marx was instead replaced by flyhalf Handre Pollard, who kicked four first-half penalties as South Africa beat New Zealand 12-11 in the final in Paris on Saturday.