The governor made the announcement in a statement he signed on Saturday.
He, however, noted that he is asymptomatic and has since isolated himself in line with Nigeria Centre for Disease Control (NCDC) protocols.
He said he has handed over the running of the state to his deputy, Kelechi Igwe.
Mr Umahi said some of his close aides also tested positive for the virus.
He however did not reveal the identities of those who tested positive.
The governor appealed to residents in the state to take preventive measures.
He added that he is working from home and will conduct all meetings virtually.
Governor Umahi joins other state colleagues who have been infected from the ailment.
These include Nasir El-Rufai of Kaduna, Okezie Ikpeazu of Abia, Bala Mohammed of Bauchi, Ifeanyi Okowa of Delta, Seyi Makinde of Oyo and Rotimi Akeredolu, Ondo.
Messrs Makinde, Mohammed and El-Rufai have since recovered.