Paramilitary troops found what they believed were missile parts after residents in the Golbasi and Mahmutlu villages in the southern province of Hatay said that objects had rained down on their fields on Friday after they heard an explosion in the sky.
The incident caused no injuries or material damage.
The Turkish foreign ministry said the Syrian ambassador was summoned and asked to provide an explanation Friday after a military investigation and eyewitness accounts suggested that the parts were that of a missile and came from Syrian territory.
"Syria said in response that the incident occurred due to a technical fault during military training exercises, expressed the government's regret over the unintentional incident caused by individual error and apologised to the Turkish government," the ministry said in a statement on Saturday.
Syrian authorities were taking measures to avoid a repeat, it added.
"The incident in question is being evaluated in detail," the statement said.
Earlier Saturday, the Turkish military had said that that it suspected the objects in question may have come from a missile originating in Syria.
Turkey and Syria share a long border, and Hatay, which is claimed by Syria, is at its western end.
The two countries have greatly improved their stormy ties since 1998, when they came to the brink of war over accusations by Turkey that Syria was sheltering separatist Kurdish militants fighting the Turkish government.
The crisis was resolved when Syria expelled Kurdish rebel leader Abdullah Ocalan and signed a security deal with Turkey, pledging to stop supporting Ocalan's Kurdistan Workers' Party, better known as the PKK.
Despite the improved ties between the two countries, two sticking points remain: the waters of the Euphrates River, which has its source in Turkey, and the status of Hatay.