Two of the blasts struck in the center of Hadda Street near the residence of former President Ali Abdullah Saleh, the news website said.
Two other explosions were heard near the Ministry of Defense.
The report did not say how many people were injured.
Elsewhere in Yemen, Shiite Houthi rebels took over a tribal stronghold in Amran, leaders of the Sunni Hashid tribe said Sunday.
"Al-Ahmar tribesmen were surrounded by hundreds of Houthi militants who attacked using heavy artillery for 7 continuous hours starting last night," said Ali al-Suraimi, a Hashid leader. "Hundreds of additional Houthi fighters reinforced those attacking the al-Ahmar fighters. They easily outnumbered the al-Ahmar tribesmen and this was key for the Houthis' success on the ground."
At least 42 people died and more than a dozen were injured Friday during clashes between the two groups, CNN reported.