The mayor of the city of half a million people, Sergei Salmin, said authorities would forcibly evacuate people from flooded zones if necessary.
He said the water level of the Ural River had risen to dangerous levels and would rise further.
“The situation leaves you no choice. At night, the river can reach a critical level,” he said. “I call on everyone in the flooded zone to leave their houses immediately.
“There is no time for convincing,” he added, saying that “those who refuse to leave the danger zone voluntarily, we will forcibly evacuate with the help of police officers.”
Kazakh President Kassym-Jomart Tokayev said the floods were one of the worst natural disasters in Kazakhstan in 80 years.
He called for authorities in the Central Asian country to be ready to help those affected.
Russian emergency services published images of rescue workers going through villages on boats and hovercrafts.
Several regions in the Urals and western Siberia have been affected by floods since the start of spring.