The Northern Irish boss is the second Premier League manager to confirm he had suffered with COVID-19 after Arsenal's Mikel Arteta also tested positive in March.
"I could hardly walk and it reminded me of walking up Mount Kilimanjaro," Rodgers told BBC Radio Leicester.
"We had a week off when we were supposed to play Watford (on March 14) and then the week after that, I started to struggle."
The 47-year-old former Liverpool and Celtic manager added his wife had contracted the virus as well.
"For three weeks I had no smell or taste. I had no strength, and a week after, my wife was the same.
"We were tested and both of us were detected with the virus."
England's top-flight clubs have agreed a provisional restart date of June 17 after the season was postponed in March due to the outbreak, with Leicester currently third behind runaway leaders Liverpool and reigning champions Manchester City.