Motiur Rahman Nizami, leader of the Jamaat-e-Islami party, was hanged at a Dhaka jail late Tuesday for the massacre of intellectuals during the 1971 independence war with Pakistan.
Turkey's ambassador to Dhaka, Devrim Ozturk, is due to arrive back in Turkey today, the news agency added.
The Turkish foreign ministry had already strongly condemned the execution, saying it did not believe that "Nizami deserved such a punishment".
It said that Turkey, which has abolished capital punishment, feared that the use of such methods risked creating "rancour and hatred between our Bangladeshi brothers".
Nizami, a 73-year-old former government minister, was the fifth and the most senior opposition figure executed since the secular government in the overwhelmingly Muslim nation set up a controversial war crimes tribunal in 2010.
Turkey had last year also furiously slammed a death sentence handed to Egypt's deposed Islamist president Mohamed Morsi who was a close ally of Ankara until he was overthrown by the military in 2013.