"You guys are acting like I have MS or something," the 26-year-old quipped to the cheering crowd at the top of Wednesday's episode of The Talk.
Sitting next to his mother, show cohost Sharon Osbourne, Jack gave an update on his condition.
"Honestly, I'm fine," he said.
But he was quick to point out that with a disease like MS, "one minute you can be fine and the next, I went blind in my right eye. It's a completely unpredictable disease."
He has since regained "about 80 percent" of his vision, but added that "they don't know if it will ever improve beyond that, but everyone's different."
And though Jack received his diagnosis only about five weeks ago, he apparently has had MS for some time.
"I guess I've been having symptoms for the last three or four years, but I didn't realize it," Jack said. "I had problems with my bladder, problems with my stomach and then, about two years ago, my legs went numb for two months and I just thought I had pinched a nerve."
Jack's diagnosis came two weeks after he and fiancée Lisa Stelly welcomed their daughter, Pearl.
"It's been good because I haven't had time to be like, 'Oh, I have MS,' because I have to change diapers and stop the baby from crying," Jack said with a smile.
And the new dad's been busy. Next up for Osbourne, he stars on the new SyFy reality series Haunted Highway, on which he and Dana Workman hit the road to investigate claims of paranormal activity in Small Town, USA. The show premieres July 3 with Osbourne and Workman in Bear Lake, Utah, while another team, Jael de Pardo and Devin Marble, poke around in Vergas, Minn.
(E! Online and SyFy are both members of the NBCUniversal family.)