ISTANBUL—Two car bombs exploded in a Turkish town on the Syrian border on Saturday, killing at least 43 people and injuring more than 100, sparking a swift warning from Ankara and feeding fears that Syria's civil war was moving on to Turkish territory.

Two huge blasts detonated in front of the municipality building and a school in Reyhanli around lunchtime, Turkey's government said, ripping through adjacent stores and carving a crater on the town's main thoroughfare. Turkish television showed images of frantic residents ferrying...