One of the explosions hit the Somalian Ministry of Education, Culture and Higher Education, according to the reports.
Meanwhile, a shooting was also reported in the same area.
No further information regarding the possible casualties were reported so far.
No groups or individuals have yet claimed responsibility for the attack.
Last week, a car laden with explosives rammed into the gate of a hotel in the center of Somalia's port city of Kismayu followed by gunfire, a police officer and a resident said.
The state-run Somali National Television said on Twitter that security forces were dealing with a "terrorist incident" at the hotel, which al Shabaab terrorist group has taken responsibility for.
"There is a blast at Tawakal hotel and there is gunfire being heard," Mohamed Nur, a police captain, told Reuters from Kismayu.
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