The 50-year-old made the announcement at a media conference alongside Bologna director Walter Sabatini.
Bologna confirmed Mihajlovic's contract will remain in place while he begins treatment.
"Unfortunately, or maybe fortunately, we did some tests and discovered some anomalies that weren't there four months ago," the former Inter Milan boss said.
"We said I had a fever and the hardest thing was to convince my wife that it was true: I have leukaemia.
"I spent the night crying and I still have tears now, but I'm not afraid. I'll go to hospital and I can't wait to start fighting. I explained to my players that I will fight to win, as I've taught them to do on the pitch.
"I'll win this challenge, no doubt about it. I want to thank all of Bologna for making me understand that I'm a member of the family, and I'll also need them to win this battle. But I'll also need to see people not crying for me. I don't want pity.
"My father died of cancer, so I always get tested regularly. If we hadn't performed these tests, I wouldn't have shown any symptoms for a year.
"None of us must think we are indestructible. All of us think, 'It won't happen to me', but when it does, it's a big shock. Your only hope then is to anticipate it, because if you discover it after two months or after a year, that makes a big difference.
"So, if I, as a famous person, can go through this, I hope it can help others to get themselves checked, to prepare and to realise that it can happen to anyone. I was perfectly healthy in every way and yet here I am.
"It changes your life in a moment. Everything changes in a moment. When you sleep and have a nightmare, you wake up, but for days you wake up and realise this isn't a nightmare, this is real.
"I hope, after winning this battle, I'll be able to talk it over with you all and look back on this period. Nothing has been given to me in life - I've had to fight for everything. I'll fight this, too."
Sabatini added: "Sinisa will hold Bologna in his hands, and Bologna will hold Sinisa, until the end of his contract.
"Whatever happens in the coming days, Mihajlovic will remain the coach of Bologna."