Croatia World Cup concern for QPR's Kranjcar
"He received initial therapy and on Monday he will travel to Zagreb for an MRI scan," Croatian football federation spokesman Tomislav Pacak reported on Sunday.
"After that we will now how serious his injury is," he added.
Kranjcar was replaced in the 33rd minute of Saturday's clash at Wembley with a left leg injury.
The 29-year-old's injury adds to Croatia coach Niko Kovac's problems as he has already had to rule out defender Ivan Strinic and midfielder Ivo Ilicevic from the finals in Brazil.
On Friday a total of 26 players left for final preparations to Bad Tazmanndorf in Austria.
Star midfielder Luka Modric who was on Champions League final duty with Real Madrid on Saturday, will meet up with the squad at a later date.
Kovac is expected to announce his final 23-man squad, in which Kranjcar was almost certainly to be named, after a friendly against Mali on May 31.
The FIFA deadline for naming squads is June 2.
Croatia start their World Cup campaign on June 12 against hosts Brazil in the opening match in Sao Paulo.
Croatia, whose best result at a World Cup was third place in 1998, have also been drawn alongside Mexico and Cameroon in Group A.