Moyes, Issa Diop and Josh Cullen were found to have contracted the virus shortly before West Ham's League Cup tie against Hull.
A club statement said: "West Ham United can confirm that David Moyes, Issa Diop and Josh Cullen have returned positive tests for COVID-19.
"The club's medical team were informed of the test results as the team were at London Stadium preparing for this evening's Carabao Cup third-round tie against Hull City. The manager and both players immediately left the stadium and have returned home.
"All three, who are asymptomatic, will now follow Public Health England and Premier League guidelines and protocols.
"Everyone at West Ham United send their best wishes to David, Issa and Josh."
Moyes' assistant Alan Irvine led the team in West Ham's 5-1 victory and suggested that the team had been "shocked" by the positive tests.
He said: "We were shocked by the news, we've had so many tests and not had any positive. But we've been very particular about protocol right from the start, the medical team are very aware of what has been happening and we've followed all the protocol, and we'll be following protocol now."
It is believed that the medical teams from West Ham and Hull were happy for the match to go ahead due to the low risk of transmission outdoors.