In his column, Mr Ünal attacked the actress' Jewish connections, saying “her father and her husband are Jewish”, calling her a “fierce Israeli advocate”.
Her father, Stephen Parker, was born to an Ashkenazi family in New York, and her husband, Matthew Broderick, was born to a Jewish mother.
While Ms Parker does not often speak about Israel or Zionism, in the early 1990s she appeared in Shalom Sesame, a Sesame Street spinoff about Israel and Judaism.
Dawn, a collection of short stories which “capture the voices of ordinary people living through extraordinary times”, was written by Mr Demirtas behind bars.
The former leader of the left-wing and pro-Kurdish Peoples’ Democratic Party, he has been detained in Turkey since November 2016, after he was accused of “leading an armed terrorist organisation”, as well as co-ordinating unlawful demonstrations.
Mr Demirtas stood to be President of Turkey from his jail cell and came third. The European Court of Human Rights has since ordered Turkey to release him.
Mr Ünal’s comments come after another ally of Erdoğan’s, Burhan Kuzu, blamed “Jewish-originated Zionist bankers” for a currency crisis which saw the lira plummet in value against the US dollar.