The Omani National Committee for Emergency Management called for the evacuations in the northern states of Barka and Saham and coastal areas including parts of the capital, Muscat, where Shaheen is forecast to strike on Sunday, bringing high winds and heavy rain.
Most of the oil-exporting country's five million people live in and around Muscat.
Oman's Civil Aviation Authority said on Friday it expected Shaheen to strengthen into a category 1 tropical cyclone within the next 24 hours, forecasting rough seas and urging residents to keep away from low-lying areas in case of flash flooding.