Sayeda Zainab district is a popular Muslim pilgrimage site believed to house the shrine of the daughter of Ali bin Abi-Talib, the fourth caliph and son-in-law of the Prophet Mohammed.
Reem Haddad, a spokesperson for the Syrian ministry of information, also said "there was absolutely no terrorist action behind the incident" on the Iranian bus.
"The bus was empty. Syrian TV showed coverage of the accident ... we saw how the tyres had been blown up," she told Al Jazeera.
"This explosion occurred as a result of a malfunction in one of the tyres ... I think they pumped too much air into the tyres"
Reem Haddad, spokesperson for Syrian ministry of information
"This explosion occurred as a result of a malfunction in one of the tyres ... I think they pumped too much air into the tyres."
Asked how a mere tyre burst could destroy an entire bus, Haddad said: "It's a big bus and it has big tyres. It is possible."
She said the explosion was "completely unrelated" to the visit by Saeed Jalilee, the Iranian national security adviser and chief nuclear negotiator, who met Syrian officials in Damascus on Thursday.
Ziad Haidar, a Syrian journalist, told Al Jazeera that there was an explosion on the bus.
"The explosion occurred as the driver and his assistant were conducting repairs on the back of the bus," Haidar said.
'Very tight security'
Al Jazeera's Rula Amin, reporting from Damascus, said: "It's very rare that we see such incidents here in Damascus. Syria controls this country very tightly; the security is very tight."
Amin said that at the news conference given by Jalilee and Syrian officials, the incident was not addressed and officials from the two countries said what the interior ministry said was enough.
Witnesses said that police and security forces quickly moved to cordon off the area.
Iran's state television reported that the bus exploded while it was refuelling at a petrol station, about 500m from the shrine.