It came during the midway point of the second half of their match with the Czech Republic, which ended in a 2-2 draw.
It will be a big blow for the Croats, who have been one of the teams of the tournament, with Modric being advised to rest in preparation for the knockout phase.
“The situation isn’t very good. He strained his adductor and may not play in the next game. He should rest and make himself ready for the second round,” team doctor Boris Nemec told Croatian television (via Football España).
“[His swollen adductor] will take several days to soothe, and the match against Spain is only in or three or four days. That won’t be enough.”
Across his first two matches of this summer’s championship Modric, a two-time European Cup winner, has created two chances and dictated much of his side’s play alongside Ivan Rakitic.
His average passing accuracy in the competition to date is 87%, and there is no doubt Croatia will miss his control of possession, especially against a side renowned for their intense pressing.
Since establishing himself at Dinamo Zagreb and then Tottenham Hotspur Modric has become a mainstay with the national team, debuting in March 2006 and subsequently winning 89 caps.
The Real Madrid star would be facing several of his club team-mates if he does indeed make the game against Spain, but may now be forced to sit out the tie to keep himself fit for the knockout rounds.