The 23-year-old has been charged with "attempting to provide material support to a designated foreign terrorist organization," which carries a maximum sentence of 20 years in prison.
The government has promised a second phase of the offensive that will go after al Shabaab in southern Somalia, the group's traditional heartland.
Somali security forces eliminated over 160 members of the extremist organization in a major operation, but analysts say that for the government to succeed, it must win the support of local clans.
The bombing on Monday targeted the Jale Siyaad military academy.
Secretary of the Somali Defense Committee Ahmed Abdi Koshin says military offensive has 'successfully dislodged' the al-Qaeda-linked terror organization from many parts of the country.
The assailants rammed the military base in the village of Hawadley with a suicide car bomb and then opened fire.
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