A regional emergencies ministry official said that "about 20 bodies" had been retrieved and rescue operations were continuing.
Spring flooding is a frequent occurrence in Central Asia but a sudden rise in temperatures following weeks of heavy snow storms has exacerbated the problem this year.
The emergencies ministry said the latest floods mainly affected two settlements, Zhylbulak and Kyzyl-Agash, where a total of about 4,000 people were evacuated to safer areas.
A powerful gush of water had also washed away a bridge on a highway connecting Almaty with the eastern city of Oskemen.
President Nursultan Nazarbayev sent a message of condolences to the families of the victims.