MetMalaysia director general Jailan Simon, in a statement, said the areas involved were Kuching, Samarahan, Serian, Sri Aman, Betong, Sarike (Pakan and Julau) and Sibu (Kanowit).
He said that the heavy rain was expected to potentially cause floods in low-lying areas in the district.
The alert or yellow level warning refers to continuous rain that is expected to occur over a period of one to three days.