The first two bombs came in quick succession and were followed by heavy bursts of gunfire by Somali security forces. The third blast took place about an hour later when a bomb went off inside a car that was being searched by the military.
There was no immediate claim of responsibility but the Islamist rebel group al Shabaab has carried out a campaign of attacks over the past two and a half years in Mogadishu, underscoring the huge security challenges the government faces.
Al Shabaab suicide bombers have targeted the Jazira hotel before, in an attack late last year.
A doctor at the Madina hospital said at least one body and 10 wounded people had been brought in.