The station played Jimi Hendrix's 'Hey Joe' after a report about the Paralympian's ongoing trial into the death of his girlfriend Reeva Steemkamp.
The track references a man shooting his girlfriend, which reflects the real-life accusation in Pistorius's court case.
The lyrics go: "Hey Joe, where you going with that gun in your hand? I'm going out to shoot my old lady, you know I caught her messing around with another man."
DJ Nemone - who is currently looking after Shaun Keaveny's show - apologised to listeners following the incident.
"In light of the nature of the news story, we apologise for any offence caused by the proximity of the song 'Hey Joe' to the bulletin," a BBC spokesperson later added. "An on-air apology was made immediately the mistake was realised."
Pistorius is facing charges of premeditated murder at a court in Pretoria, South Africa earlier today.
The athlete admitted to shooting Steenkamp, but denied murdering her, saying he had mistaken her for an intruder.