Sir Brian, 78, is a long-time animal rights activist and founded the Save Me Trust which campaigns for the rights of foxes and badgers.
He previously resigned as the RSPCA's vice president over the 'appalling' animal welfare standards in farms certified under its 'assured' scheme.
Sir Brian told the Daily Mail, 'I wouldn't do Glastonbury next year because of the politics of the people who run it, unless that changes, I won't do it.
'They like killing foxes and badgers, and they think it's for sport and that's something I cannot support because we've been trying to save these badgers for years, and they are still being killed for years, so that's the reason we're missing out on it.'
The world-famous music festival is going through a fallow year but the founder Sir Michael Eavis, 90, who is also a dairy farmer, previously called May a 'danger to farming' and criticised him for his opposition to the badger cull, which is aimed at preventing the spread of bovine TB.
When asked if the rock band had turned it down repeatedly, May said: 'I don't think the conversation of us doing has ever taken place because they know how I feel.'
