Afghan Police and the NATO-led international coalition were unable to confirm the cause of the explosions, though it was rumoured that there could be a Taliban hand involved.
India's Ministry of External Affairs said in a statement that the embassy was not the target and all the Indians present in the premises are safe.
The area has been cordoned off by the police.
It is the second explosion to hit Kabul in just over a week.
There were also reports of gunfire, even as security forces rushed to the scene of the multiple blasts, which occurred at about 4:00 p.m. local time on Friday.
"There has been explosion in an area which is close to the NDS (intelligence agency) hospital and APPF (Afghan Public Protection Force) headquarters, we are investigating," Kabul police spokesman Hashmat Stanikzai was quoted, as saying.