The club announced the news shortly before the fourth-round clash at Stamford Bridge and assistant manager Arno Michels stated that the positive result came back on Friday.
Tuchel will now follow Covid isolation guidelines and will be unable to join his squad in flying to the Club World Cup in Abu Dhabi after the match.
However, Chelsea confirmed that he intends to travel to the Middle East when allowed to do so.
Their Club World Cup semi-final takes place on Wednesday, February 9 against Al Hilal or Al Jazira, with the final scheduled for the following Saturday.
Palmeiras, Al Ahly or Monterrey await in the final if the Blues qualify, with a third-placed play-off game scheduled for the same day between the losing semi-finalists.
NHS guidelines state that people who have tested positive for Covid can leave isolation after five days if they can provide two negative tests and do not have a high temperature.
On Tuchel’s Club World Cup chances, Michels told BBC Sport: “We will see what happens in the coming days.”