Petrović played as a shooting guard, and achieved prominence in the 1980s and early 1990s. The pro clubs he played for included: Šibenka, Cibona, Scavolini Pesaro, Novi Zagreb, and Racing Luxembourg. He was among the 105 player nominees for the 50 Greatest EuroLeague Contributors list.
Petrović has coached the senior men's Croatian national team on three occasions, in 1995, when they finished third in the EuroBasket 1995, between 1999 and 2001, when they finished 7th in the EuroBasket 2001, and during Croatia's run to the Olympics in Rio 2016.
Between 1991 and 1995, Petrović started his club coaching career with Cibona. Between 1995 and 1997, he coached the Spanish ACB League club Caja San Fernando, before returning to Cibona for the 1997–98 season.
In the 2001–02 season, he went to Poland to coach Anwil Włocławek. In 2004, he was again in Spain with Caprabo Lleida. In 2006, he took over at the Italian League club Carifac Fabriano, before switching to Eurorida Scafati. In the 2007–08 season, he took over the Croatian club Zadar. He then became the head coach of Cedevita.
He was named the EuroCup Coach of the Year in 2011.
In February 2012, he was appointed as the coach of Bosnia and Herzegovina's senior men's national basketball team.
After departure of Božidar Maljković, Petrović once again took charge over Cedevita on November 26, 2012. After Cedevita was eliminated from the EuroLeague and the Croatian Cup, and left without any chance of qualifying for the ABA League Final Four, Petrović offered his resignation to the club, which was accepted on 3 March 2013.
On March 23, 2016 Petrović was named as the coach of Croatia national team in third term.
In third team as a head coach of Croatian national team, Croatian team played in a qualifications in Torino, Italy for the 2016 Summer Olympics. Croatia was qualified.
In the 2016 Olympics in Rio de Janeiro, Croatia beat Spain, and played in a quarterfinal of tournament against Serbia. Serbia won 83–82.
On September 15, 2017 Petrović was sacked after debacle on EuroBasket 2017 against Russia, in round of 16.
Aleksandar Petrović was born in Šibenik in family of Biserka Petrović (née Mikulandra and born in 1941), who is from village of Bilice near Šibenik, and Jovan Petrović, who was born in Trebinje, Bosnia and Herzegovina.
Petrović is the older brother of the late professional basketball player Dražen Petrović, who died in a car accident in 1993. Petrović's close cousin is Serbian former professional basketball player Dejan Bodiroga.
He was training on basket ground in your street Preradovićeva in hometown Šibenik, where was training retired professional basketball player and coach Neven Spahija, Aleksandar's late brother Dražen and ever many players, who aren't professional players. Aleksandar and Drazen are well famous croatian basketball players. He is in a relationship from 1985, with Jadranka Petrović, and he has daughter Lina.