The former Liverpool defender who became a Sky Sports sports expert also said his aunt was treated at the hospital last week for the same reason, but is now recovering well.
Carragher made the admission in his latest column for The Telegraph, where he was discussing a potential return date for football in the UK.
He said: “Like everyone else, I think that the return of football must be conditional.
“No one needs to tell me that the health of the people closest to us matters most. My wife, Nicola, tested positive for Covid-19. My aunt was in the hospital with Covid-19 last week and is recovering.
“So even if I can’t wait for the games to come back, it goes without saying that no one wants decisions made for the wrong reasons at the wrong time, contrary to government and scientific advice. “
Carragher went on to explain that while health and safety should be the primary concern of decision makers at the top of the game, sporting integrity should be the second most important consideration.
A number of football figures are skeptical of the resumption of the current season, including West Ham vice president Karren Brady, who previously called for the campaign to be canceled.
This would benefit West Ham, which is in the midst of a relegation battle.
Former Carragher club Liverpool would also miss the Premier League title despite 25 points ahead and only two wins after being crowned champion.
UEFA announced this week that it wanted to reward the team’s performance during the season on the basis of “sporting merit” and urged the best European leagues to “explore all options” before the possibility of ‘cancel the season comes into play.
Carragher welcomed the announcement and has now called on the Premier League and the Football League to follow suit.
Coronavirus in sport
He also argued that the coronavirus will not go away in August, so suggestions that the current season should end now to protect the next are irrelevant.
The German Bundesliga is considering a return to action on May 9, which could set an example for other European leagues.
Carragher added, “We may never get a fully satisfactory conclusion for this season, but there is no reason why we cannot get a fair conclusion. “