The Polish border control refused the Nigerian striker entry after an issue with his documentation.
His 19 goals last season enabled the Foxes to compete in Europe's second tier competition.
Leicester boss Rodgers said: "We've had an issue with Kelechi. His documentation coming into the country wasn't sufficient, so he wasn't able to travel. He will be unavailable for the game.
"The paperwork didn't allow him to enter the country. We'll have to look at that when we're back."
Jonny Evans has not travelled, while Wilfred Ndidi is banned.
Legia top Group C after beating Spartak Moscow 1-0 in their opening game while Leicester lost a 2-0 lead to draw 2-2 with Napoli.
"They had a fantastic result in the last game. They're very well organised, the players are very committed, and on the counter-attack they can give us problems," Rodgers said at a press conference.
"In the last game and a half we have been more like ourselves in our football, so hopefully we can bring that to Legia and make it really difficult for them.
"You travel to play in great stadiums in front of passionate supporters. It should be a great game in a great atmosphere, and it's something you always have to deal with away in Europe.
"It's been a great experience and we want to keep achieving it. It's an ambition of ours to keep playing at this level. You have to earn it and that's hopefully something we can keep doing over the next number of years."