The fighting broke out on Wednesday after police used water cannons on hundreds of protesters who had blockaded the agency's headquarters in the provincial capital Banda Aceh since late Tuesday.
One person was hit by a flying stone and at least one police car was damaged.
The 2004 tsunami killed or left missing at least 216,000 people in 11 Indian Ocean nations, more than half of them in Aceh on the northern tip of Sumatra island.
Tens of thousands of people still without permanent homes have complained that the process is too slow given the enormous resources committed to the province.
Protesters, many of whom still live in wooden barracks, demanded that the Aceh reconstruction agency should speed up the building of homes and businesses.
Mirza Keumala, a spokesman for the agency, promised to do everything possible to speed up the process.
But he also alleged that a local aid group called the Barracks Forum had organised the rally, and was demanding that funds be directly transferred to its own account, something he said the agency could not do.