Its funding, by revenue from phone voting in shows like Strictly Come Dancing and The Voice, has significantly diminished.
"More and more people are voting for free with a touch of the button," said BBC Arts Director Jonty Claypole.
Since it was set up in 2003 the fund has distributed £5m in grants to emerging talent.
Launching as the Fame Academy Bursary, it supported more than 1200 individuals in the performing arts.
Beneficiaries have included global singing sensation Adele, composer Mark Simpson and the Bristol Old Vic.
"I owe the start of my career to this incredible charity - devastating times," tweeted Irish actor Fra Fee, who starred in the big screen adaptation of Les Miserables.
Before it closes, the fund will award £156,100 split between 17 alumni.
Claypole insisted that, despite the closure, "the BBC's commitment to the arts and nurturing talent remains as strong as ever."
The BBC Performing Arts Fund will close after 13 years in March next year, it has been announced.