All three had been condemned to death for murder, police chief Abdi Mohamed told AFP, with one of the men allegedly taking part in an assault on the presidential palace last month.
The executions come three days after another Somali MP was assassinated by Shebab guerrillas in the capital, the fifth this year, as the militants step up their attacks in Mogadishu to counter claims that their insurgency is waning.
"Three Al-Shebab members including the one who facilitated the last attack on the presidential palace were executed this morning," Mohamed said.
Two other Shebab militants, who allegedly confessed to killing a student who worked for an NGO, were publicly executed in the capital on July 15.
The Somali government, which only controls part of the war-ravaged country, executed 15 people in 2013, according to Amnesty International, while another 19 people were executed in the self-declared autonomous region of Puntland in the northeast.
Human Rights Watch (HRW) has severely criticised the "unequal" way military courts are run, with normal procedures not followed. They claim the tribunals -- which the country's fragile government uses to try Shebab rebels -- had condemned dozens of people to death last year.