Following Zadar's relegation from the top flight at the end of the 2004–05 season, he became a first-team regular during the club's time in the Croatian second division.

In the summer of 2008, he was loaned to Hajduk Split[2] and immediately became a regular at the club, appearing in all of their 18 league matches in the first half of the 2008–09 season.

In Monaco's last Ligue 2 match of the 2011–12 season, he scored the winning goal from a free kick in a 2–1 away victory over Boulogne.

[9] Subašić missed the beginning of the 2019–20 season due to a hamstring injury and was replaced by Benjamin Lecomte, who joined Monaco in July 2019.

However, Lecomte continued to play in the starting formation despite poor performances, even after Subašić had recovered for his injury.

[13][14] Subašić made his international debut with the Croatian under-21 national team, in a friendly match against Denmark on 1 March 2006.

During the same year, he won a total of 6 international caps with the team, including two competitive appearances in the qualifying for the 2007 European Under-21 Championship.

[15] In 2009, he was called up to the Croatia national team at the full international level, and made his debut for the team on 14 November 2009 in a friendly match against Liechtenstein in Vinkovci, playing the full 90 minutes and keeping a clean sheet in Croatia's 5–0 win.

Subašić received praise for his performance at the tournament, including from legendary German goalkeeper Oliver Kahn.

[36][37][38] Subašić wears the image of his former NK Zadar teammate, Hrvoje Ćustić, under his jersey while playing.

The decision was made by FIFA as a result of previous players taking off their jersey and displaying images or texts that could cause controversy.

[40] Following the match against Russia, Subašić walked up to the fans in order to take off his jersey and display the image once again, although he only showed a small part of it, as he was stopped by Croatia staff member Iva Olivari, whom he proceeded to hug afterwards.