The law, introduced by Labour in 2004, bans the use of dogs to hunt foxes and other wild mammals in England and Wales.
May told BBC’s Andrew Marr Show she had received a “clear message” on the issue and said there will not be a vote during this parliament.
Michael Gove has prioritised animal welfare issues since May appointed him Environment Secretary after the June election.
But Jeremy Corbyn repeatedly criticised May for saying she was in favour of fox hunting during the election, which shattered the PM’s authority after the Tories lost their Commons majority.
The Tories had pledged in their manifesto to hold a free vote on a Bill in Government time to allow Parliament to decide the future of the Hunting Act 2004, the Press Association reported.
However, May told the BBC: “As prime minister, my job isn’t just about what I think about something, it’s actually about looking at what the view of the country is.
“I think there was a clear message about that and that’s why I say there won’t be a vote on fox hunting during this parliament.”
The move was welcomed by campaigners.
Animal protection organisation, Humane Society International UK, said it was “heartening”.
Director Claire Bass said: “It can never be acceptable in a modern, progressive society to sanction the chasing and ripping apart of a live animal for the sake of entertainment, and it is heartening that that message has been heard loud and clear.
“However, we cannot be complacent, so we encourage animal lovers to keep telling their MPs that they won’t vote for cruelty, and to urge action by the government to clamp down on the illegal hunts still taking place.”
But the decision could provoke a fierce backlash from the Tories’ traditional supporters.
Tim Bonner, chief executive of the Countryside Alliance, told HuffPost UK last month that the Conservatives should not take the support of rural areas for granted.
In a blog on this website, Bonner wrote of campaigns to retain the ban on fox hunting: “Opening the door to this sort of animal rights campaigning would be questionable at the best of times, but at this stage of the Brexit process when the creation of an agricultural policy to replace the Common Agricultural Policy should surely be the priority it seems especially strange.”