The full extent of the problem is yet to be diagnosed but Ranieri has claimed that the 28-year-old could be out for "some time".
"Sneijder has not travelled to Moscow and this is a blow for us," Ranieri is quoted by ESPN as saying upon arrival in the Russian capital.
"My fear is that we will lose him for some time because his injury seems more serious than we first expected. We will wait to see what the doctors say."
The Blue and Blacks began their Champions League campaign with a 1-0 home loss at the hands of Trabzonspor.