Career
Džudović began his football career in 1999 by joining his first club, Jezero Plav which is a Montenegrin club In 1999 he made his debut in the club"s fourth division of Yugoslavia "Ezero." With the help of the club rose to the third (2001), and a year later and the second division championship of Yugoslavia. In 2003, Džudović joined another Montenegrin club FK Jedinstvo Bijelo Polje but just making 14 appearance and scoring 2, he left to join Serbian club OFK Beograd but just only made 1 appearance and helped the club qualify for the Intertoto Cup, the first time the club qualified for a European Cup in 30 years.
In 2004, Džudović left OFK Beograd to join a Ukrainian side Volyn Lutsk and signing a three-year contract with the team
Džudović made his debut in the Ukrainian Premier League was held March 27, 2004 in a victory for the "Volyn" match against Karpaty Lviv. In Spring 2005 in a match against Dynamo Kyiv, Džudović received a serious injury that gave rise to early termination of the contract.
In less than three seasons in the "Volyn" Miodrag spent 44 games in which scoring one goal. In 2006, Džudović joined a Russian club Spartak Nalchik, signing a contract with a local club
Miodrag debut in the Russian Premier League took place on March 18, 2006 in the first round match against the CSKA Moscow which they lost 1–0.
On 26 March 2006, Džudović scored his first goal for the club and scored in the Premier League against Spartak Moscow in a 2–2 draw. He is Spartak"s captain as of 2007. In Opening match of league 2010, Džudović made his 100th appearance for the club against Anzhi Makhachkala which had Džudović T-shirt on the back.
In November 2014, Džudović left Football Club Irtysh Pavlodar after one season with them.
His good performance in Russia led Montenegro manager Zoran Filipović called up Džudović into the squad and eventually he scored his first goal for national team on his debut against Macedonia on 19 November 2008 and also played 90 minutes in the game. Džudović made headlines when Džudović was the player Wayne Rooney kicked during a Euro 2012 qualifier that resulted in a three-game ban (the entire group stage of Euro 2012) for the Manchester United and England national team striker.
At first, it was known that Rooney would miss at least one match in the opening round of the first phase at Union of European Football Associations Euro 2012. After the game with Montenegro, Rooney sent a personal letter to Union of European Football Associations in which he apologised and expressed regret for the tackle on Džudović which earned him the red card.
Džudović has said Rooney does not deserve a three match ban and that Rooney is a great player.
Džudović also plead to reduce Rooney’s Euro 2012 ban.