Istanbul prosecutors said in a statement they would examine the recording of the Friday night edition of the Beyaz Show on Kanal D and would also investigate the programme's producer and presenter.
The controversy has erupted as the military presses on with its campaign against the outlawed Kurdistan Workers' Party (PKK) in the Kurdish-majority southeast, which the government says is aimed at flushing out militants but activists claim has killed dozens of civilians.
"Are you aware of what is happening in the east of Turkey?" the caller asked.
"People are fighting with hunger and thirst, in particular the children. Please be sensitive and do not remain silent. Please have some kind of sensitivity as a human," she said.
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Pro-government Twitter users expressed outrage over the comments on the channel, which is owned by the Dogan Group, one of Turkey's biggest conglomerates.
"Our channel, which has always stood with the state against terrorism, is deeply saddened that it became the target of a provocation."
Turkish media reports said that Diyarbakir prosecutors had also opened an investigation against the "supposed teacher AC" on suspicion of making "terrorist propaganda" for the PKK.
The education ministry also said there were only three teachers working in Diyarbakir named Ayse -- a very common name in Turkey -- and none of them appeared to be the person who called the show.
The leader of the pro-Kurdish Peoples' Democratic Party (HDP) Selahattin Demirtas strongly defended the producers and the caller, saying all she had done was to "give a message of peace".
"And then the whole mechanisms of the state get set into motion, the programme makers get lynched and this women is pursued," he said.