On 1 February 2011, Swiss Super League club FC Basel announced signing Dragović on a four-and-a-half-year contract.

Dragović played his domestic league debut for his new club in the home game in the St. Jakob-Park on 12 February 2011 as Basel won 3–0 against FC St. Gallen.

Dragović scored a goal in the second leg of quarter-final matches against Tottenham Hotspur, whom they beat 4–1 on penalties after a 4–4 aggregate draw to progress to the semi-finals.

Dragović missed solely the second leg of the semi-final at Stamford Bridge due to a yellow card suspension, but had played in all the other European ties.

After Servette had equalised, Dragović headed home a corner, taken by team captain Alex Frei, to the 2–1 final score.

But referee Sascha Amhof understood this as rude gesture against the Servette fans and showed the scorer a yellow card.

[13] In the 2012–13 Swiss Cup Basel reached the final, but were runners up behind Grasshopper Club, being defeated 4–3 on penalties, following a 1–1 draw after extra time.

In that season he helped Dynamo reach the last sixteen of the UEFA Champions League for the first time in 16 years, getting knocked out by Manchester City 1–3 on aggregate.

[17] On 31 August 2017, Dragović joined Premier League club Leicester City on a season-long loan from Bayer Leverkusen.

He was called up for the national team of Austria for their 2010 FIFA World Cup qualification match against Romania, but due to an injury he was unable to play.

He made the final squad for Euro 2016, where he was sent-off in the first game against Hungary,[20] and missed a penalty in the decisive match against Iceland, which ended in a 2–1 defeat.

[25] After making further comments about being reluctant to apologize—stating that "on the inside everybody knows, so I believe, that it was very, very much fun doing it"—Dragović reportedly traveled to the Bundeshaus in Bern in order to personally apologize to Maurer.