Police said the blasts hit the gate of the Criminal Investigation Department headquarters before militants stormed the building. Spontaneous gunfire could be heard, Xinhua news agency reported.
The Al-Shabaab militant group claimed responsibility for the attack. The group, which is fighting against the Somali government, frequently stages attacks in Mogadishu.
"There were two huge bombings near Somali's CID headquarters. I have seen black smoke rising from the place," a witness said.
The death toll could rise as the injured were in critical condition, a police official told Xinhua. The CID headquarters is located alongside on a busy road.
Al-Shabaab, which means "The Youth" or "The Youngsters" in Arabic, is a terrorist group based in East Africa.
The group battles with the UN-backed government in Somalia and has carried out a string of attacks in neighbouring Kenya.
Allied to Al Qaeda, the group has been pushed out of most towns it once controlled but it remains a potent threat to peace and stability in the region.
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