The 25-year-old was set to feature on a world title double-header at the Casino de Monte-Carlo in the principality, live on Sky Sports Action.
Fury was aiming to return to winning ways against Czech fighter Sour, after his defeat against Alexander Povetkin at the O2 Arena in August.
A short statement from Matchroom Boxing read: “Due to a virus Hughie Fury has unfortunately had to pull out of his fight tonight in Monaco.”
The bill is topped by Alexander Besputin’s battle with Radzhab Butaev for the vacant WBA welterweight belt and the undisputed world title fight between new Matchroom star signing Cecilia Braekhus and Victoria Bustos.
British and Commonwealth champion Joe Cordina can remain unbeaten in an 11th fight and add the WBA continental super-featherweight belt with victory against Mario Tinoco.