Two other soldiers and two delivery staff were injured.
The attack on the base was followed by the shooting dead of a police officer which was claimed by the Continuity IRA, another group that split from the IRA after a ceasefire was agreed with the British government in 1997.
Police are questioning three other men over that killing.
Thousands of people attended the funeral of Constable Stephen Carroll on Friday.
Politicians from both the republican and unionist - supporters of British rule - camps have condemned the attacks and vowed to continue to work together in the province's government.
The two sides agreed to share power in 2007 with Sinn Fein, a republican group with strong links to the IRA, joining the Democratic Unionists in government.