Kovacic only returned to training on Monday following a month out with a hamstring injury but has been hit with another setback.
Chelsea manager Thomas Tuchel announced the bad news on Tuesday, with the European champions also set to miss the likes of Jorginho and N’golo Kante.
"We have bad news because Mateo was in training yesterday and with a big smile and it was a pure pleasure to have him back," said Tuchel.
"But he tested positive today, for coronavirus, so he's quarantining for a few days. So it's a huge setback for him personally and for all of us."
Asked if the resurgence of coronavirus has caused extra concerns at Chelsea generally, Tuchel added: "Yes, I was aware that this can happen, me personally.
"I'm not happy not only as a manager but also as a person. But this is the reality at the moment, we have to face it to be ready to adapt and to do the best thing possible to avoid transmission."
Kovacic has made 12 appearances across all competitions for Chelsea this season, scoring one goal and providing five assists.
The Croatia international’s absence could see Saul Niguez drafted into the side after a difficult start to life in England following a loan switch from Atletico Madrid.
