The 34-year-old has scored 11 goals in 18 Premier League appearances this season, with only Son Heung-min, Harry Kane and Mohamed Salah above him in the scoring charts.
Vardy has averaged a league goal approximately every 134 minutes, a rate that only six players can better this term, although he has not found the net in any of his past five appearances.
Rodgers is therefore confident Leicester's season will not be badly impacted by the loss of Vardy as it prepares for a run of matches that includes meetings with Everton, Leeds United, Wolverhampton Wanderers and Liverpool before the first leg of a UEFA Europa League Round of 32 tie with Slavia Prague.
"Jamie Vardy will be out for a few weeks," Rodgers said. "As you know, we've been managing him over this last number of months, and he's been absolutely fantastic.
"We have a window now that allows him to have a minor operation on his hernia and then he'll be back within a few weeks. He'll be out for that period.
"It's one that doesn't keep him [Vardy] out for too long, but it's just a repair in and round that hernia area. It's one we feel he can't really put it off much longer.
"We were hoping to do it a few weeks back, but this is a window where we can get it done and that will obviously leave him with a good part of the season where he can be really influential for us."
Leicester, which is two points behind league leader Manchester United, travels to Brentford in the FA Cup fourth round on Monday (AEDT).