Strinic, 31, played in six of Croatia's seven games at the World Cup including the final where they lost 4-2 to France. He joined Milan from Sampdoria on a free transfer in the close season and has yet to play for his new club.
Milan said the heart condition, which the club named as cardiac hypertrophy, was discovered during routines tests.
The club said the exams were "worthy of further study to be carried out after a period of rest. For this reason, the player must temporarily suspend sporting activity until the completion of the exams".
Strinic has also played for Hajduk Split, Dnipro Dniporpetrosvk and Napoli and has won 49 caps for Croatia.
(Reporting by Brian Homewood, editing by Ed Osmond)
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