Ono, whose first notable Capcom project was Dino Crisis 2 in 2000, was rushed to hospital while on the Asian leg of a promotional tour for the crossover fighting game.
Capcom confirmed that the executive's physical condition "heavily deteriorated" and that he would "not be performing work-related affairs for a while".
Speaking to fans on Twitter, Ono announced that another person would be in charge of the Street Fighter franchise, but that he would continue to support it.
"I'll refrain from work for current job for a while. Another person in charge of SF series for a while. Of course I'll constant support to it," Ono tweeted.
"I'll be out of the limelight as fighting game series for a while. I'll think about the new future of fighting game after this. ;D" he added.
Ono previously worked on the Resident Evil series, before serving as producer on Street Fighter IV, Super Street Fighter IV and Street Fighter X Tekken.
Street Fighter X Tekken was released for the Xbox 360 and PS3 earlier this month. A PC and PlayStation Vita version will release later this year.
A Namco follow-up, titled Tekken X Street Fighter, is also in the pipeline, although no release date has been announced.
> Read our Street Fighter X Tekken review
Watch a trailer for Street Fighter X Tekken below: