SANA news agency said The first blast occurred by a suicidal who blew up a belt at the entrance of Assayidah Zainab town while the second was by a booby-trapped car at al-Tin Street in al-Diyabia town.
SANA said eight people were martyred while, 13 others were injured by the attacks.
The Syrian Observatory for Human Rights, a British-based monitoring group, reported a higher toll of at least nine people killed and 30 wounded in the blasts.
The last attack on Sayyeda Zeinab on April 25 killed at least seven and wounded dozens.
A string of bombings carried out by Takfiri group, ISIL, near the shrine in February left 134 people dead, most of them civilians, according to the Observatory.
And in January, another attack claimed by ISIL killed 70 people.