"The incident was reported yesterday afternoon and an investigation was launched immediately," Nis police spokeswoman Lidija Pavlovic said.
"The explosion created a crater in the lawn and we are currently establishing the details," she added.
Stojkovic's mother Desanka was in the house at the time but was not injured in the incident.
In a statement to Belgrade media, Stojkovic, the manager of Japan's Nagoya Grampus Eight, said he was not the target.
"It leaves a bitter taste but anything I might say at this point in time would be superfluous because I am convinced that I wasn't the intended recipient of this assault," he was quoted as saying by Belgrade's B 92 website.
"I will let the police do their job and I have complete faith that they will establish who was behind this attack as well as what the motives were," he said.
The 46-year-old Stojkovic captained the former Yugoslavia to the 1990 World Cup quarter-finals after winning two league titles with Red Star Belgrade.
He came to loggerheads with die-hard Red Star fans as the club's president in 2007 when he sold a plethora of talented players to keep the debt-ridden club afloat and stepped down after steering them to two successive league and cup doubles.
In a most recent incident, several Red Star fans ejected Stojkovic out of the team stadium's cafe last month and told him never to come back to the ground where he once drew standing ovations as a player.
