Kvržić started his professional career at Proleter Teslić, before joining HAŠK in 2009.
Kvržić made his senior international debut for Bosnia and Herzegovina in 2011, earning 8 caps until 2020.
Kvržić started playing football at a local club, before joining the youth setup of his hometown team Proleter Teslić.
[6] He won his first trophy with the club on 13 May 2014, by beating Dinamo Zagreb in the Croatian Cup final.
[12] In January 2020, Kvržić was transferred to Turkish outfit Kayserispor for an undisclosed fee.
[14] On 13 September, he scored his first goal for Kayserispor against Kasımpaşa, which secured the victory for his squad.