Petrovic's decision came in the wake of his side's Euro 2012 qualifying failure. The 1-0 defeat to Slovenia meant Serbia missed out on a play-off place after finishing third in Group C behind runaway leaders Italy and second-placed Estonia.
After a meeting of the Serbian FA's (FSS) executive board, it was announced Curcic, previously Petrovic's assistant, will stand in for the two games against as-yet unnamed opponents, allowing more time to find a full-time successor.
"The FSS has appointed Radovan Curcic as the interim coach for the national team's two friendlies in November against opponents yet to be determined," the FSS said on its official website.
"The new coach will be named after elections within the FSS."