"We are still investigating the motive behind the attack," Kawedar told the Associated Press.
He said seven police officers could not stop the attack and it took several hours for back-up to arrive.
There have been no arrests so far.
Situated on the northern tip of Sumatra island, resource-rich Aceh was torn by conflict for nearly 30 years before the December 2004 tsunami spurred a peace agreement between the government and the separatist Free Aceh Movement (GAM) in August 2005.
More than 15,000 people were killed in the conflict while 160,000 died in the tsunami in Aceh alone.
Irwandi Yusuf, a former GAM separatist, took over as the governor of the province last year, further cementing the peace deal, but there have been sporadic incidents of violence since, often over the sharing of resources in the province.