Oke died in Abuja on Saturday at the age of 51, Channels TV reports.
Details of his death are, however, yet to be clear.
Oke came into the limelight in 2017 when he won the Nigeria Prize for Literature for his book, The Heresiad.
He was presented with a cheque of $100,000 (N37m) by the Nigeria Liquefied Natural Gas Company Limited.
His poems and other writings have appeared in journals, anthologies and other publications worldwide.
He has performed his poems at various fora in Nigeria, South Africa and the United States.