A recent sighting of three beavers in the River Otter was said to have been the first of its kind for centuries.
The Department for Environment, Food & Rural Affairs (Defra) said they could be carrying a disease "not currently present in the UK".
Environment Minister George Eustice said the government was considering "the best way" of rehoming the animals.
The beavers have been spotted at several places along the River Otter, between Budleigh Salterton and Ottery St Mary.
In a Parliamentary answer, Mr Eustice said: "We intend to recapture and rehome the wild beavers in Devon and are currently working out plans for the best way to do so.
"All decisions will be made with the welfare of the beavers in mind."
He added there were "no plans to cull beavers".
Beavers were hunted to extinction in England and Wales during the 12th Century.
Lorna Douglas, 36, who filmed a beaver on the Otter last year, said the animals should be left alone.
"They are not damaging the river and they are not hurting anyone," she said.
"We are really privileged to see them in the wild."
Defra said: "Beavers have not been an established part of our wildlife for the last 500 years.
"Our landscape and habitats have changed since then and we need to assess the impact they could have."
Devon Wildlife Trust is carrying out an experiment in west Devon to see if beavers could help restore wetland areas.
Beavers living wild in Devon are to be caught and "rehomed" in captivity, the government has said.