Born in Zadar, Popović is the son of Petar, a retired basketball player and a present-day basketball coach. Marko started training in basketball in the youth school of KK Zadar, in 1991, but his family moved to Zagreb in 1994, when the father signed with Benston. 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.
Popović played with the youth junior squad of KK Zadar in the 1998–99 season, and also played in 3 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. After spending a year in the United States, playing college basketball at the College of Southern Idaho, he moved back to Croatia and Zadar in 2001. In the 2002–03 ABA League season, Zadar surprisingly won the ABA League championship, after beating Maccabi Tel Aviv in the finals. Popović played a major role in his team's success, and he was awarded with the MVP title of the leagues' final four tournament, which took place in Ljubljana. In 2003 he moved 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 2005 Popović was signed by the Turkish League club Efes Pilsen, and the next year, he moved to Žalgiris Kaunas of the Lithuanian League, with which he won both the 2006–07 and 2007–08 Lithuanian League season championships. While playing with UNICS Kazan, he was named the Finals MVP of the 2nd-tier level European-wide league, the EuroCup, in 2011. In 2011 he returned to Žalgiris. After leaving Žalgiris in June 2013, Popović agreed to contract terms with the Russian VTB United League club Khimki Moscow Region, as he signed a two-year deal with the club on 7 August 2013. On 16 June 2015, he left Khimki, after spending two seasons with the club. On 6 October 2015, he signed with the Spanish club Baloncesto Fuenlabrada. In February 2017 he became the all-time EuroCup scoring leader, but was surpassed by Bojan Dubljević and Rafa Martínez later same season. On July 17, 2018, he re-signed with the Spanish club Baloncesto Fuenlabrada. After spending four seasons in Fuenlabrada, in May 2019, Popović announced he will retire from professional basketball on the end of the season.
