The 41-year-old said in a statement released by Denmark's TV3, for whom he works as an expert commentator, that he was diagnosed last week with a mild form of lymphoma.
"Naturally, I'm shocked about the diagnosis, but I'm also clear that I now have a fight ahead of me - a fight I will win," Laudrup said in the statement.
"I've had very optimistic reports from the doctors, and I intend to continue as an expert commentator for TV3."
During a professional career lasting 14 years, Laudrup played for nine different clubs, winning the Scottish title three times during a four-year stint at Rangers.
Laudrup, who scored 21 goals in 82 games for Denmark, joined TV3 on his retirement from football in 2000.
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