Born in Zadar, Popović is the son of Petar,[2] a retired basketball player and present-day coach. Marko started training in basketball in the youth school of KK Zadar, in 1991, but his family moved to Zagreb in 1994, when his father signed with Benston.[3] Popović then entered the youth system of Cibona, where he remained until 1997, when his family moved back to Zadar. Popović's cadet team won the national championship, and he was voted the MVP of the tournament.[3]
Popović played with the youth junior squad of KK Zadar in the 1998–99 season, and also played in three games with the club's senior team that season. In the club's youth squad, he scored an average of 25 points per game, which earned him a spot in the top-tier level senior men's team of the club in the following season of 1999–00.[3] After spending a year in the United States, playing college basketball at the College of Southern Idaho (NCAA Division II), he moved back to Zadar, Croatia, in 2001.[3]
In 2003 he moved to Pamesa Valencia of the Spanish ACB League for the 2003–04 season, where he stayed until February 2004, before moving back to Croatia again, this time to Cibona, with which he won the Croatian League championship in the 2003–04 season.
In 2011 he returned to Žalgiris.[5] After leaving Žalgiris in June 2013, Popović agreed to contract terms with the Russian VTB United League team Khimki Moscow Region, as he signed a two-year deal with the club on 7 August 2013.[6] On 16 June 2015, he left Khimki, after spending two seasons with the club.[7]
On 6 October 2015, he signed with the Spanish team Baloncesto Fuenlabrada.[8] In February 2017, he became the all-time EuroCup scoring leader,[9] but was surpassed by Bojan Dubljević and Rafa Martínez later same season.[10] On 17 July 2018, he resigned with the Spanish club.[11] After spending four seasons with Fuenlabrada, in May 2019 Popović announced he will retire from playing professional basketball at the end of the season.[12]