The clashes occurred ahead of a cabinet decision on whether or not to extend martial law in the province.
The soldier died and three of his colleagues were wounded during a firefight with Free Aceh Movement (GAM) rebels late on Friday afternoon in the Banda Alam area of East Aceh, said military spokesman Lieutenant Colonel Ahmad Yani Basuki.
That deadly battle followed a mid-afternoon firefight in East Aceh's Idi Rayeuk area that left two government soldiers wounded, Basuki said.
On Monday the cabinet of President Megawati Sukarnoputri is to discuss whether or not to extend the martial law status imposed for six months on 19 May when government forces began an all-out offensive to crush GAM.
The military has suggested that its operation, the biggest since the 1975 invasion of East Timor, should continue.
In other violence a suspected insurgent, Bahar, 45, died during an exchange of fire with government troops in West Aceh on Thursday, Basuki said.
Also, humanitarian workers recovered the bodies of three unidentified men in Aceh Besar district on Friday, one of the volunteers said. Two of the corpses were found in a river with signs of severe beating, the volunteer said.
More than 900 Acehnese guerrillas have been killed in the battle over Aceh
More than 900 Acehnese insurgents and 67 police or soldiers have been killed during the operation, according to military figures.
More than 1800 insurgents have been arrested or have surrendered, the military says.