The German-born Hungary defender has been on the German national bone marrow donor registry for the past six years and was recently found as a match for a blood cancer patient.
"He could now give another human being a second chance," the club said in a statement.
Orban, who has missed training since Sunday to prepare with special injections, will undergo the harvesting procedure on Wednesday.
Leipzig said it was unclear if he would feature in their league match against Union.
"I without a doubt wanted to make the donation as soon as possible," Orban said. "I have the chance to potentially save another person’s life with very little effort. It was a no brainer. I hope my donation will help the recipient to recover from their illness.
"I might of course miss the Union game but even with my sporting ambitions, football is of secondary importance," he added.
Leipzig are in fourth place on 36 points, three behind Union and four off leaders Bayern Munich.
