Angola, Namibia and Botswana use the river for transport and irrigation
Twenty villages in Botswana have been evacuated after the Okavango River burst its banks.
Water in the river, which starts in Angola, passes through Namibia and empties into Botswana's Okavango swamp, has reached unprecedented levels.
Officials in Botswana have called for a joint intervention to prevent the spread of waterborne diseases.
A BBC reporter says there are concerns that another result of the flooding is the spread of snakes and crocodiles.
Angola, Namibia and Botswana all use the Okavango for fishing, transport and irrigation for farming on the river banks.
The BBC's Letlhogile Lucas in Botswana's capital, Gaborone, says more than 200 families have been moved to higher ground.
But the Okavango's water levels are expected to continue rising in the coming days, which could make it difficult for officials to provide services, he says.
Tracy Molefi at Botswana's Department of Water Affairs said it was important for the three countries to work together.
"Where there is co-operation, incidences of conflicts are well managed because then we are talking already," she told the BBC's Focus on Africa programme.