The 22-year-old left-hander, who was acquired by the Tigers in a trade with the Toronto Blue Jays at the 2015 deadline, shared the news via his Instagram account.
Norris said he was diagnosed with a malignant tumor on his thyroid after being optioned to Triple-A Buffalo in April. He learned of the diagnosis while shuttling between Buffalo and Toronto for additional testing.
Tigers general manager Al Avila confirmed via text to ESPN.com that the team was aware of the diagnosis before making the trade for Norris with the Blue Jays. Avila said the club expects him to make a full recovery.
"Hearing this was alarming, yea," Norris said in his Instagram post. "Weird, yea, that too. I was given the option to shut my year down & get it removed immediately. However, seeing another doctor that determined I could wait until the end of the season reassured my gut feeling. Just Keep Playing. Baseball kept me sane."
Norris, from Johnson City, Tennessee, said playing baseball helped keep his mind off his medical situation and buoyed his outlook.
Blue Jays outfielder Dalton Pompey was Norris' teammate in Toronto and in the minors. He said he knew Norris was dealing with something.
"I knew that something was up because I remember him telling me that he went to the doctors for something in his throat," Pompey said before the Blue Jays hosted the Royals in Game 3 of the ALCS. "I didn't think anything of it. He said not to worry about it, and now, obviously, it's escalated into something else."
Norris indicated he wasn't sure whether to share the news but said he believed in the power of prayer in overcoming the diagnosis.
"Regardless of results on the field, I forgot about it when I was between the lines. After all, I was just trying to get the heck out of AAA. & I did. I was revived with an opportunity, a blessing from God, with the Tigers back in the Big Leagues," Norris said.
Norris (3-2, 3.75 ERA) is regarded as one of the Tigers' most promising young pitchers. He is expected to compete for a spot in the team's starting rotation next season.
"So yea, the power of prayer," Norris said. "It got me through this season. Now that it's over, it's time to get this thing out, so please keep me in your thoughts & prayers as I undergo surgery & come out 100% cancer free!"
Information from The Associated Press was used in this report.