Despite efforts by a team at Tophill Low nature reserve near Driffield to control the creature, which has been breeding in the wild since the late 1950s, their numbers are at their highest in more than a decade.
Large numbers of water vole appear to have attracted mink, which also eat rabbits, ducks, chickens, fish and frogs, from far and wide.
Next March the reserve is hoping to coordinate a 10-day purge, working with adjacent landowners and wildlife groups, who will be asked to monitor “mink rafts”, to trap mink, which will then be put down.
Warden Richard Hampshire said mink had already seen off water vole across large swathes of the UK, and it would be a “real shame” if the River Hull corridor, traditionally a stronghold for native species, lost its water voles.
He said: “If we walked away and left them to it, they would become extinct in the next few years.”
A lot of the river Hull is no longer managed because of Government cuts, and rafts installed some years ago had “fallen to bits”, adding to the problem.
Salmon paste, apparently a favourite for mink, is being tested in the traps.
Usually a couple of mink are spotted on the site every year, but in September they found four and the latest footage from cameras installed as part of a study on otters has picked up several more, putting the total for the year at around 10.
The American mink are thought to have originated from the animals brought to Britain for fur-farming in the 1950s. By December 1967, mink were found in over half the counties of England and Wales.