Salad Ali Jelle, deputy defence minister, blamed Thursday's suicide car bombing on al-Qaeda members.
The only casualties were people killed inside the car, Jelle said by phone, adding he did not know how many died.
A witness contradicted Jelle's account, saying he saw wounded Ethiopian soldiers at the scene.
Hundreds of Ethiopian soldiers live at the base, which is surrounded by a low wall and has an ungated entrance.
"The situation is Somalia has gone from bad to worse after the intervention of Ethiopian troops"
Abed, Kumasi, Ghana
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The latest clashes come weeks after four days of ferocious fighting killed 1,000 people at the end of March, and a truce since then has failed to prevent sporadic clashes.
At least seven people also died on Wednesday in separate fighting.
The Ethiopian backed interim government has been attempting to maintain order in Mogadishu against resistance from fighters loyal to the Islamic Courts' Union and from the local Hawiye clan after their forces drove out the Islamic courts from large areas of the country that the conservative group controlled.
Also on Thursday, an Ethiopian military truck exploded on the outskirts of Mogadishu, possibly killing the soldiers on board, said a witness, who did not know what caused the explosion.
The truck was one of two carrying Ethiopian soldiers travelling on the main road to key southern Somalia towns.
The explosion took place about 20km south of Mogadishu.