In a Twitter post, the ministry said Saturday's attack on a bus terminal killed ten and wounded more than 15 others. Turkey's state-run Anadolu news agency later gave a higher toll of at least 18 dead and 27 wounded, citing the defence ministry.
Several cars and buildings were damaged in the attack, which involved two bomb-laden vehicles, according to Anadolu.
Meanwhile, the Britain-based Syrian Observatory for Human Rights, a war monitor, said 19 people had died in the blast, 13 of them civilians. The group said 33 people were wounded, some of them seriously.
Since 2016, Turkey and its Syrian rebel allies have mounted three separate military operations in northern Syria against "terrorist elements", seizing control of the border area, including al-Bab.
There was no immediate claim of responsibility but the Turkish defence ministry said on Twitter that "inhumane and uncivilised PKK/YPG terrorists continue to target innocent civilians".
Ankara considers the Kurdish People's Protection Units (YPG), a group forming the backbone of the Kurdish-led Syrian Democratic Forces (SDF), an extension of the Kurdistan Workers' Party (PKK), which has waged a decades-long armed campaign against the Turkish state for autonomy.
The PKK is designated a "terrorist" organisation by Turkey, the United States and the European Union.
Turkey's latest push into northern Syria came last month when it launched a military operation aimed at pushing back the YPG-led SDF from the border region east of the Euphrates River and establish a "safe zone" stretching at least 30km (19 miles) into Syria to resettle some of the 3.6 million refugees it hosts.