Tickets for the league leaders' final home game were offered for £15,000 a pair via an online re-sale website.
The 7 May match against Everton, which could see the Foxes crowned champions, sold out in 90 minutes on Monday.
"The club has a duty of care to its supporters and is working diligently to prevent ticket touting," a Leicester City club statement said.
"As a result, a small number of season-ticket holders and members have this week received multi-year bans."
The club said this prevents those responsible from attending Leicester games, as well as having their season tickets cancelled "without compensation".
The Foxes are seven points clear of nearest rivals Tottenham and need three wins from their five remaining games to guarantee the title.
They host West Ham on Sunday then Swansea and visit Manchester United ahead of the game against Everton, before finishing the season away to Chelsea.