According to the state-run Anatolian news agency on Sunday, the explosion occurred in the port city of Mersin - where a well known celebrity was performing on the last day of a local music festival.
Two police officers were among the wounded and were in critical condition.
Turkish television pictures showed people in bloodstained clothes being carried away from the scene of the blast.
Bomb disposal experts destroyed a second suspicious package at the venue.
Organisers of the Candan Ercetin concert had expected about 30,000 music fans to attend.
No claim of responsibility has been made, and it is not clear whether the attack was carried out by Kurdish separatists, leftists or an Islamist organisation – groups that have bombed Turkish cities in the past.