The 31-year-old moved to San Siro over the summer on a free transfer after playing a key role in Croatia's march to the World Cup final.
However, a routine physical carried out this week has put the full-back's career in jeopardy after he was diagnosed with a heart condition.
"AC Milan inform that during routine medical tests, carried out on all professional athletes in Italy, it was found that Ivan Strinic suffers from the beginnings of hypertrophy in the cardiac muscle which will need further tests following a rest period," the club confirmed in a statement published on their official website.
"The player must therefore suspend temporarily all competitive sporting activity until the follow-up exams have been completed."
Strinic played for Sampdoria and Napoli in Italy prior to joining Milan.