Barnes was expected to miss up to six weeks of action when he suffered the injury in a 3-1 defeat to Arsenal in late February.
Before suffering the injury, Barnes was arguably Leicester’s player of the season, as he had struck 13 times and provided four assists in 35 appearances across all competitions.
Leicester will however have to make do without the 23-year-old as they continue their push for a Champions League spot next season.
"He's had a slight setback," Rodgers said of Barnes, who made his England debut in October.
"He's just gone in to have a second minor operation to clear up some of the damage in his knee. That will rule him out for the rest of the season. The plan is to get him fit for pre-season.
"It's a shame [he will miss the Euros] because he has been outstanding. The most important thing is to get his knee right."
England manager Gareth Southgate is due to name his squad for this summer’s European Championships next month but one name that will be missing from his 26-man squad will be Barnes.
