The operations are part of a wider offensive against the militant group, which has been waging an insurgency in Somalia for over a decade.
One Somali soldier was also killed in the fighting.
The government spokesman said the military operation is ongoing and that Al-Shabaab will be "removed from their places in that region" in the next few hours.
He called on the people living in the cities of Elbur and Galhareeri to stay away from the group's bases.
The offensive against Al-Shabaab is being supported by the African Union Mission in Somalia (AMISOM).
AMISOM has said that it is committed to helping the Somali government "restore peace and stability" in the country. (ILKHA)