The mortar rounds were fired near a stadium, Lieutenant Colonel Wilson Rono, AFRICOM spokesman, told Reuters.
Earlier on Thursday, al-Shabaab militants set off a suicide car bomb at a checkpoint about 15 kilometres (nine miles) outside the capital. At least five people were injured including soldiers, police officer Ali Roble told Reuters.
A second police officer, Abdullahi Nur, told Reuters that many vehicles had been parked at the checkpoint for inspection when the blast occurred.
Al-Shabaab frequently carries out bombings in Mogadishu and elsewhere in Somalia in their effort to bring down the Western-backed federal government and drive out the AMISOM forces defending it.
On Friday, twin car bomb blasts in Mogadishu claimed by al-Shabaab killed 45 people.
Abdiasis Abu Musab, al-Shabaab’s military operations spokesman, told Reuters the group was responsible for both the mortar attack and the car bombing.