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.
The Federation of Socialist Youth Associations (SGDF) is reported to have had at least 300 members staying at the Amara Culture Centre in Suruc, where the explosion happened.
The young people had been planning to travel to Kobane to help with rebuilding the town.
A video released on social media apparently showed the moment of the blast, at a news conference taking place in the centre’s garden.
In the video, a group of young people are chanting slogans while holding the federation’s flags and a large banner with the words: “We defended it together, we are building it together.”
Then an explosion rips through the assembled youngsters.
Graphic images of the aftermath show bodies littering the ground, with the red flags being used to cover them.
The district governor of Suruc, Abdullah Ciftci, said: “The fact that it is a suicide attack increases the possibility that IS is responsible.
“We think the attacker was a woman.
“Preliminary findings show that she was acting on her own,” he told BBC Turkish.