The central England side, who have not won since beating Manchester United 5-3 in September, announced on their website (www.lcfc.com/) that Robinson's contract had been terminated.
"Current Academy Director Jon Rudkin will assume the responsibilities of Director of Football," the statement added.
Manager Nigel Pearson may now be feeling he has some breathing space with the promoted side's troubles being pinned on recruitment before the season.
Of 10 new signings, only forward Leonardo Ulloa and midfielder Esteban Cambiasso have had any real impact on the first team with the former struggling for goals after an initial purple patch.
The Foxes, who count Gary Lineker among their most high profile fans, lost 1-0 at home to champions Manchester City on Saturday and have not won in 11 league games.
The Thai-owned club are three points adrift at the bottom on 10 points from 16 matches.
(Writing by Mark Meadows, editing by Alan Baldwin)
