The WHO office in Damascus did not immediately respond to a request for comment and the Kurdish-led administration did not provide further evidence of the reported infection.
In the statement, the regional administration said a 53-year-old man had died at a hospital in Qamishli on April 2 and that a sample was sent to Damascus and tested positive for COVID-19, the lung disease caused by the coronavirus.
But it said health authorities in the northeast had not initially been made aware of the results.
An official at the Qamishli hospital, which falls under the control of Syria's central government in Damascus, denied the existence of any coronavirus cases so far at the hospital.
Relief organisations have expressed concern about the coronavirus pandemic reaching northeastern Syria, where health infrastructure has been shattered by war and medical supplies are limited.