The 31-year-old only joined the Italian club in July and is yet to make an appearance for the Rossoneri.
Strinic has been a Croatian senior international since May 2010, earning 49 caps for his country. He was part of the Croatia team that reached the World Cup final in Russia this summer, starting in six of the seven matches in the tournament.
According to his club Milan, the player must "suspend temporarily all competitive sporting activity," after he was found to have the heart condition.
The heart problem was reportedly found during a routine check, with the Italian side reporting that further tests would need to be carried out.
Prior to his summer move to the San Siro, Strinic played for a number of teams in his native Croatia and Ukraine, as well as in Italy.
He began his career at hometown club Hajduk Split as a youth, returning to the senior squad after spells at Le Mans' B team in France and fellow Croatian club Hrvatski Dragovoljac.
Strinic made the move to Ukrainian side FC Dnipro in January 2011 for a reported fee of €4m and made 85 league appearances in three-and-a-half years at the club.
The Croatian international swapped Ukraine for Italy in 2015 when he joined Napoli, where he spent two seasons before a switch to fellow Serie A side Sampdoria in August 2017.
After one year at the Genoa club he made the move to Milan on a free transfer this summer.