Ankara voiced fury at the headline broadcast on screens at the airport which said Turkey allowed sex with children under the age of 15.
"This headline tarnishes the image of Turkey, and is false," a Turkish diplomat said after the Austrian envoy was summoned to the ministry on Saturday.
The headline said "Türkei erlaubt Sex mit Kindern unter 15 Jahre" (Turkey allows sex with children under 15 years.)
An Austrian Foreign Ministry spokesman confirmed Turkey had summoned its charge d'affaires on Saturday evening. "We take notice of the reaction of the Turkish authorities, and this is for us a matter of freedom of the press," Thomas Schnoell said.
A spokesman for Vienna airport said that while the news ticker was on its premises, it was not responsible for its contents. "(It) is operated by an Austrian newspaper, which has editorial responsibility over its content," the spokesman said. "The airport does not have any influence over its contents."
The Turkish constitutional court last month ruled in favour of removing an article in the criminal code which characterizes all sexual acts with a child of less than 15 years of age as "sexual abuse", a decision condemned by civil society groups.
According to a report in the English-language Turkish newspaper Hurriyet Daily News, the ruling is seen as a "calamity" for the rights of children in the country, amid concerns that "child abusers will start walking around freely because there is no new regulation [to fill the void]."
Swedish Foreign Minister Margot Wallstrom waded into the row on Sunday, tweeting: "Turkish decision to allow sex with children under 15 must be reversed. Children need more protection, not less, against violence, sex abuse."
The news ticker, which was a report from the Austrian newspaper Kronen Zeitung, was removed from Vienna airport's screens following Ankara's complaint, Turkish news agency Dogan reported.
According to Turkish newspaper Daily Sabah, Austria was negligent in allowing such a headline to be displayed, especially given the history of the former archbishop of Vienna, Cardinal Hans Herman Grör, who allegedly abused over 2,000 young men.
"Turkey is a state that aims to protect and develop universal human rights and as a respected member of the international society, Turkey is committed to international agreements and protocols in terms of children's rights" the Turkish foreign ministry said, and added that Turkey is aware of its responsibilities in this regard.
The age of sexual consent in Turkey is 18 years, under its civil code.
The incident came little more than a week after a similar row over another ticker displayed at the airport, in which the same newspaper declared: "If you go to Turkey, you are supporting (Turkish President Recep Tayyip) Erdogan."
This message was also taken down following a complaint from Turkish authorities.
Relations between Ankara and Vienna have taken a dive in recent days, with several Austrian ministers speaking out against Turkey's longstanding bid to join the European Union, particularly in the wake of the massive purge that followed the July 15 coup bid.