His office said the ex-monarch, which is currently in Switzerland, has a cancer which has spread and chronic leukaemia, and has recently undergone surgery.
"In recent weeks I have been informed of a serious medical diagnosis," Michael, who was forced to abdicate by Romania's communist regime in 1947, said in a statement.
"I am sure my daughter Margareta will have the wisdom and strength to represent me and to carry out all my public duties."
The former king is undergoing treatment "which prevents him from making public appearances," his office added, saying Michael needs "a period of recuperation."
Born on October 25 1921 in Sinaia, 120 kilometres (75 miles) north of Bucharest, Michael reigned twice, between 1927 and 1930 and then from 1940 to 1947, before the communists ended the monarchy in the Balkan country.
A descendant of the German Hohenzollern dynasty, he long dreamed of "serving" his people again.
After moving back to Bucharest in 2002 he led a low-profile life, making only brief appearances in public notably for his birthday and for religious festivals.
Romania saw the return of democracy in 1989 with the collapse of Nicolae Ceausescu's dictatorship.
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