According to officials on Friday the crocodiles were washed into rivers.
Crocodile farmers, locals and police have trapped thousands of the reptiles, using plastic bands to tie their legs behind their backs and then piling them into pick-up trucks.
The flood gates at the Rakwena crocodile farm close to the Botswana and Zimbabwe borders were opened on Sunday because it was feared that rising flood waters would crush the reptiles, releasing some 15 000 crocodiles into the Limpopo River.
"At night time we have more success. It is much easier to see them," Zane Langman, whose in-laws own the farm, told the media.
Most of the crocodiles are less than two metres long. The area is home to several farms that supply crocodile skins to the fashion industry.
Avoiding the water
"We are working as a team with the stakeholders," police spokesperson Brigadier Hangwani Mulaudzi said on Friday. There have been no reports of injuries caused by the escaped reptiles.
Police in Zimbabwe, on the other side of the Limpopo, also issued warnings to people to avoid going into the water because of the crocodile threat.