"The BBC does not currently have any weather presenters who are disabled and we are actively seeking to improve on screen diversity.
"You don't need to be an expert or have a qualification in meteorology."
Staff are said to be "furious" at the positive discrimination and some said they were "shocked" when they saw the ad.
The "politically correct job vacancy" has been blasted with some saying the "box-ticking exercise" sounds like a story line from the BBC's own spoof comedy W1A.
In a recent episode of the show, bosses hired Muslim Sadiq Iqbal as a weather presenter because they wanted a bearded man to keep the broadcasting watchdog happy.
A source told The Sun: "This feels like political correctness gone mad on the part of the BBC.
"Surely it's much more important for the weather to be presented by an expert, rather than someone with a disability?
"Everyone supports disabled people getting great jobs but it makes sense that they still have the right experience and qualifications. This feels like a box-ticking exercise.'
"W1A is meant to be a parody, not a documentary."
The BBC has traditionally employed fully-qualified meteorologists and many of its current crop have a wealth of experience.
Weatherman Alex Deakin has an Astrophysics degree, Chris Fawkes has a Geography degree, Peter Gibbs is a polar meteorologist and Philip Avery is a navy weather expert.
Many familiar faces had previously been employed by the Met Office - including Michael Fish who famously dismissed an oncoming hurricane in 1987.
The job advert said the BBC Academy would be running a free training opportunity to help men and women with a disability feel comfortable presenting bulletins on television and radio.
Candidates will be given a masterclass with current weather presenters as well as sessions with a voice coach.
They will even be given a session with stylist along with training presenting using an earpiece and live talkback.
"You will meet established weather presenters and members of the production team and will learn what it takes to present BBC weather bulletins," it said.
Candidates who take part in the training will be eligible to apply for future vacancies.
A BBC spokesperson said: 'We are not advertising for a disabled weather presenter. This training opportunity is open to men and women with disabilities who have a passion for weather and the environment and who have the potential to become weather presenters in the future.
"There are no jobs guaranteed at the end of the training. There is nothing 'PC' about offering training to people with disabilities."
- Daily Mail