Digital music sales at Apple Inc.’s iTunes store have fallen 13% to 14% world-wide since the start of the year, according to people familiar with the matter, underscoring the fragility of the music industry’s nascent recovery.

The dive in download sales is stark compared with a much shallower dip last year. Global revenue from downloads fell 2.1% in 2013, according to the International Federation of the Phonographic Industry, but that decline was offset by increases in revenue from ad-supported and subscription streaming services, resulting in overall digital revenue growth in most markets last year.