The explosions occurred at the pro-Kurdish People's Democratic Party final election rally in Diyarbakir, the main city in Turkey's predominantly Kurdish southeast, as the party's leader Selahattin Demirtas was preparing to address the crowd.
Rally organisers urged calm, saying a malfunctioning power distribution unit caused the explosions, but witnesses said there were two separate blasts spaced by five minutes that they believed were caused by bombs.
The explosions come at a tense time, two days before Sunday's parliamentary elections in Turkey, in which the Kurdish votes will be critical.
That would scuttle the AKP's ambitions to introduce a new constitution and change Turkey's parliamentary system into a presidential system that could give President Recep Tayyip Erdogan executive powers.
Prime Minister Ahmet Davutoglu said authorities would investigate the cause of the explosions.
"Whatever is behind this incident, whether it was a power transformer explosion, an assassination attempt, an act of provocation, we shall investigate it," he said.
Demirtas urged calm and asked supporters not to "respond to provocations.
