The reality star received the news just three weeks after welcoming baby daughter Pearl Clementine with his fiancée Lisa Stelly.
Jack has now appeared on his mum Sharon Osbourne's daytime chat show The Talk to discuss how he is coping with MS, revealing that he went blind in his right eye from the disease.
"Honestly, I'm fine," Jack told host Julie Chen. "Ultimately that is the toughest thing with this disease that I'm learning - one minute you can be fine, and the next I went blind in my right eye. It's a completely unpredictable disease."
Revealing that he has since regained 80% of vision in his eye, he explained: "They don't know if it will ever improve beyond that, but everyone's different.
"Some people are left with a blind spot, some people's return 100%, some people never even get anything back, so it's hit and miss."
Referring to their newborn daughter and Jack's positive mindset, fiancée Stelly said: "We don't have much time to be sad because we have a little girl and diapers to change. So we're having fun, we're going to be okay."
Jack quipped: "You guys are acting like I have MS or something!"
Sharon previously broke down during a recent taping of The Talk as she addressed Jack's condition.
"[Jack's] doing really, really good and I want to thank everyone for all their texts and goodwill and love they send to us," she said.
"It's been amazing for Jack because I really believe that... prayer really helps."