[8] Kjær made his senior debut for Midtjylland in the Viasat Cup training matches in June 2006,[9] Two months later, he signed his first professional contract, keeping him until 2009.

[15][16] Kjær made his Superliga debut on 30 September 2007, in the 2–0 victory against AGF[17][18] By October 2007, his performances attracted the likes of Premier League clubs Middlesbrough and Chelsea.

[28][29][30] In February 2008, Kjær signed a five-year contract with Italian club Palermo, effective from the summer 2008,[31][32] earning Midtjylland a €4 million transfer fee.

[46][47][48][49] Due to his physical strength and tenacity, Kjær's performance continued to improve and was named the second best player under 21 in Serie A by La Gazzetta dello Sport.

[56][57][58][59] Kjær confirmed his reputation as a first team regular in the 2009–10 season, and formed a strong defensive partnership with fellow centre-back Cesare Bovo.

[68] He was named 2009 Danish Talent of the Year in November 2009, beating Arsenal's Nicklas Bendtner and Ajax's Christian Eriksen after his successful first season in Palermo.

[73][74][75][76][77] After serving a one match suspension, Kjær returned to the starting line-up against Fiorentina on 24 January 2010 and helped the club keep a clean sheet, in a 3–0 win.

[94] Both national coach Morten Olsen and the player, himself, agreed that the move to Wolfsburg was not only economically justifiable for the young Danish defender but also the shift that this was a step in the right direction for his development.

[123][124][125][126] Italian side Roma revealed the club were on the verge of signing Kjær on a €10 million move from Wolfsburg as a replacement for centre-back Philippe Mexès who left for AC Milan on a free transfer.

[132] However, in a 2–1 loss against rivals, Lazio on 16 October 2011, he received a straight red card in the 50th minute for a foul on Cristian Brocchi, resulting in a penalty and was successfully converted by the opposition team.

[139] On 11 January 2012, he returned to the starting line–up for Roma's match against Fiorentina in the Round of 16 of the Coppa Italia and helped the side keep a clean sheet, in a 3–0 win.

[152][153][154][155][156] After his loan-spell at Roma ended, Kjær stated he would not return to Wolfsburg, after coach Magath decided the Dane was not going to be part of his first team plans for the club's 2012–13 season.

[162] After missing the follow-up match against Hannover 96 due to a potential transfer to Galatasaray, which later collapsed, Kjær returned to the starting line-up against FC Augsburg on 16 September 2012, as they drew 0–0.

[194] Since making his debut for the club, he quickly established himself in the starting eleven, playing in the centre-back position, forming a partnership with Marko Baša.

[221][222] Kjær then kept three consecutive clean sheets in the first three league matches, including scoring his first ever Ligue 1 goal against Lorient with a deflected free kick.

[241][242][243][244][245] Following a transfer speculation over the summer, it was announced on 16 June 2015 that Kjær joined Turkish side Fenerbahçe, signing a four-year deal for €7.65 million.

[246][247][248] Kjær made his Fenerbahçe debut, starting the whole game, in a 0–0 draw against Shakhtar Donetsk in the first leg of the UEFA Champions League third round.

[324] Kjær started in the next five matches for Sevilla since returning from injury and proved to be instrumental as he helped the club beat Manchester United in the second leg of the UEFA Champions League Round of 16.

[349][350][351][352] However, just like Martin Škrtel (his former teammate at Fenerbahçe who signed and terminated his contract with Atalanta within August 2019), he failed to convince the team's head coach Gian Piero Gasperini.

[356][357] On 13 January 2020, Kjær signed with AC Milan on loan for the rest of the 2019–20 season, with the option to make the transfer permanent for an undisclosed sum.

[363] After missing one match due to illness, Kjær returned to the starting line-up, playing in the centre–back position, losing 4–2 against rivals, Inter Milan on 9 February 2020.

[369][370][371][372][373] He would make 11 more appearances for Milan (9 in Serie A and 4 in Coppa Italia) before the club bought him out from Sevilla for €3.5 million on 15 July 2020, the expiry date of the buy-out clause in his loan deal.

[390] Kjær was an unused substitute for the friendly match against Greece, and returned to the under-21s for a single game in March 2009,[391] playing well enough that under-21 coach Keld Bordinggaard recommended him for a recall to Olsen's squad.

[397] Kjær was once again a part of the senior squad for the 2010 FIFA World Cup qualification game against Sweden on 6 June 2009 after Per Krøldrup was unavailable due to injury.

[399] Kjær established himself in the Danish starting line-up, played the following three qualification games, and helped Denmark qualify for the 2010 World Cup despite facing injury along the way.

[400][401][402][403][404] For the September 2009 qualification game against Portugal, Kjær told reporters that Cristiano Ronaldo should be stopped by a series of small fouls and one hard tackle.

[406] On 28 May 2010, Denmark coach Morten Olsen announced that the player would be part of the final squad of 23 participating in the 2010 FIFA World Cup in South Africa.

[415] Following Denmark's win over Iceland in the UEFA Euro 2012 qualifying, Stig Tøfting criticised his performance, as he witnessed him for making too many mistakes during the match.

[419][420] The next two years saw the player regaining his first team place for the national side and helped them qualify for the UEFA Euro 2012 following their 2–1 win against Portugal on 11 October 2011.

[457][458] He helped the national side keep four consecutive clean sheets in friendly matches between 22 March 2018 and 9 June 2018 against Panama, Chile, Sweden and Mexico.