The 19-year-old Chelsea forward tested positive last week, not long after Arsenal manager Mikel Arteta also received confirmation he had contracted COVID-19.
Chelsea responded by partially closing their Cobham training base, with first-team players and coaches forced to self-isolate as a measure.
Blues boss Frank Lampard said that three-time capped England international Hudson-Odoi was on the road to recovery.
“I’m happy to say that in Callum’s case, he has made great progress and almost feels his usual self, which is obviously the news we all want to hear,” Lampard said.
“I’m aware that not everyone can or will recover from this virus, so I urge the football and sporting community to continue to act responsibly and look out for the health of others.”
The English Premier League has been suspended until April 4 at the earliest, amid Chelsea’s bid for a top four berth.
“We still don’t know when competitive football will restart, but it isn’t worth worrying about that too much at the moment,” Lampard said.
“We all miss football but right now it’s about acting responsibly and in the best interests of society.”
Ironically, Chelsea closed commercial sites at Stamford Bridge on Wednesday, including stadium tours and the club museum.