Malatya Gov. Aydın Baruş told reporters that "around 15 people" were believed to be in the building when it collapsed.
Rescuers have been searching for any other signs of life under piles of debris.
Gov. Baruş said that of the 13 injured people, two are in intensive care, whereas seven others have been discharged from the hospital.
Deputy Interior Minister Ismail Çataklı later told reporters they have not yet received any reports confirming that there were still people trapped under debris. "There is no report of anyone missing," he said.
The Malatya Chief Public Prosecutor's Office announced that four people had been detained in connection with the incident, including the owner of a business where a renovation was taking place.
"In the face of collected evidence, it has been understood that unauthorized renovation was being made. The owner of the business and three employees have been detained," said the prosecutor's office in a written statement.
According to eyewitnesses, a pillar was demolished as part of the renovation works.
The building had a coffeehouse along with other shops on the ground floor, increasing the chances of casualties as more people were present at the time of the collapse.