Authorities said a car loaded with explosives rammed the gates of a building housing the embassy in Mogadishu and blew up Saturday.
Levent Gumrukcu, a Turkish Foreign Ministry spokesman, said an agent and two of three attackers died in the bombing, the Hurriyet Daily News reported.
The injured agents, one in critical condition, arrived in Ankara Sunday.
Somali Islamic al-Shabaab militants claimed responsibility for the attack.
"Mujahedin forces in Mogadishu have just carried out an operation targeting a group of Turkish diplomats in Hodan district," the al-Qaida linked group said on Twitter.
Turkish Prime Minister Recep Tayyip Erdogan condemned the attack and noted that Turkey has been helping Somalia, the newspaper said.
In 2011, Turkey sent economic and humanitarian aid to war-torn Somalia and was one of a few countries to set up an embassy there, the newspaper said.
Erdogan visited Somalia later the same year.
The weekend bombing was also condemned by the United States, the Organization of Islamic Cooperation and Somali President Hassan Sheik Mohamud, the newspaper said.