The authorities were trying to determine the identities of the victims, Erzurum deputy governor Ibrahim Yurdakul told Anatolia news agency.
Civil defence workers managed to rescue five people, including two children, who were stranded for about an hour in a shop, Anatolia reported.
Many houses in the city were inundated, and the authorities were planning to accommodate affected residents in a government building, Yurdakul said.
Floods and landslides claimed seven lives in the northern Black Sea provinces of Trabzon and Rize last week.