Around 100 others were wounded in the explosion, which may have been caused by a female suicide attacker from the Islamic State group, officials say.
Kobane has seen heavy fighting between IS militants and Kurdish fighters.
It was retaken by the Kurds from IS forces earlier this year.
Turkey's Prime Minister Ahmet Davutoglu said initial findings suggested the attack was the work of IS.
"Turkey has taken and will continue to take all necessary measures against Islamic State," Mr Davutoglu told a news conference in Ankara, according to Reuters.
"Measures on our border with Syria... will be increased," he added. (+BBC video) » | Monday, July 20, 2015
