Writing on his Facebook page, Jack revealed his worries about whether the disease would affect his ability to perform in the gruelling competition.
"When I first signed up to do Dancing with the Stars, one of the first questions I was asked was 'how will having MS affect your ability to perform throughout the season?'" said Jack. "The truthful answer is… I had no idea."
The popular contestant, who was cheered on by his mother Sharon Osbourne in his show debut, explained that since his diagnosis, he has maintained a very active, healthy lifestyle. Jack has fortunately not suffered any severe symptoms during the competition, apart from the "odd bit of tingling" down his leg and the "occasional bout of fatigue".
The dancing star, however, who is married to Lisa Stelly, admitted that he couldn't tell what his limitations would be.
"You never really do know what tomorrow is going to bring," said Jack. "The truth of the matter is, today I'm good. I'm feeling strong and confident in my ability to continue on."
The 27-year-old then went on to say that his goal was to win the dancing competition, and thanked his professional dancing partner Cheryl Burke for her support.
"I'm not saying everyone with MS can do DWTS, but it doesn't mean you can't set an achievable goal and strive to achieve it every day. No matter who you are or what you struggle with, that is something we are all capable of. And right now my goal is to win that mirrorball trophy.
"I'm ready to sprint. I owe a lot of that to my partner Cheryl Burke. Cheryl believes in me in a way that has made me believe in myself."
Jack then gave a special mention to his fans at the end of his post, which was "liked" by more than 33,360 people. His message clearly hit home for some who responded saying they could relate to him.
"I can't quite put into words how moved I am by all the people who have reached out to me online. It truly means a lot," said Jack.
"Just know this, if that day does come where I do win this mirrorball, know that I didn't just win it for me, but I won it for all of us with MS."