Modric limped off in the second half of Croatia's volatile 2-2 draw with the Czech Republic in a match marred by crowd trouble as Croatian flans threw flares on to the pitch and clashed with each other in St Etienne on Friday.
"Modric's groin is strained and swollen," Nemec told Croatian media on Saturday.
"He will train at less than full intensity in the next few days and is very unlikely to be available for the Spain match," he said.
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Defender Vedran Corluka, who needed stitches after a clash of heads during Croatia's opening 1-0 win over Turkey, is also doubtful after the injury recurred against the Czechs and forced him to wear a water polo cap in the second half.
Several other players, including striker Mario Mandzukic and winger Ivan Perisic, who scored Croatia's first against the Czechs, are expected to shake off minor knocks in time for the match with Spain.
(Writing by Zoran Milosavljevic; Editing by Ian Chadband)
