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Due to being symptomatic, the 21-year-old will likely miss out of Germany's upcoming international games.
"It showed up in the UEFA testing on Monday," Lampard said at Stamford Bridge. "We retested yesterday when we found out.Clearly everyone else in the squad is negative, so that is a good sign. I've spoke to Kai a couple of times since we found out.
"He's at home, he's isolating and he was very disappointed because he wants to play. He had some minor symptoms yesterday, his symptoms have escalated slightly today but he is fine. I spoke to him two hours before the game today and he's disappointed to be out.
"He's trying to do all the right things. It's just one of those things in the modern day with where we're at. Hopefully he isolates, does the right things and comes back firing."
Chelsea could have Havertz back after the international break when they face Newcastle United upon their return to Premier League action later this month.
In the absence of Havertz, Timo Werner and Tammy Abraham formed a formidable attacking combination against Rennes, and Lampard was pleased with their performances.
He said: "The link up was good. I know Timo, from the many conversations I've had with him, that he is comfortable on the left side. In the early stages of the season we had one fit out-and-out winger. Christian Pulisic, Hakim Ziyech were out and Callum Hudson-Odoi was getting match fit.
"We have options but those options were tight at the beginning of the season. I know Timo can do it and he gives the chance for Tammy or Oli to give their attributes as a central striker.