The English Football League (EFL) on Sunday said there were two positive cases out of the 1,014 COVID-19 tests taken by players and staff at Championship clubs.
Hull later announced both individuals, who have not been named, came from the struggling East Yorkshire club and will self-isolate for a week before being tested for a second time.
A club statement said: "Hull City can confirm that two people have tested positive for COVID-19 following the first round of testing at the training ground.
"Medical confidentiality means the names will not be disclosed, and the club asks for this to be respected.
"The duo, who are both asymptomatic and feeling no ill effects, will now self-isolate for seven days – in line with the protocols set out in EFL guidelines – before being tested again at a later date.
"The club will continue to liaise closely with the affected personnel and will make no further comment."
According to the Daily Telegraph, Hull have written to EFL chairman Rick Parry and the other 23 clubs in the Championship to express fears over the season potentially resuming next month.
Championship teams are preparing to resume training from Monday, albeit while following specific protocols laid down by league organisers.
It is unclear if the Championship campaign will resume. No fixtures have been played since March 8, with Hull reportedly the first second-tier club to outline a belief that it is too risky to get the action under way again.