The bulletin on the digital station Radio 6 Music on Tuesday was followed by the Jimi Hendrix Experience’s version of Hey Joe.
The song begins: “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”.
A BBC spokeswoman said: “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. An on-air apology was made immediately the mistake was realised.”
South African athlete Pistorius was in court in Pretoria on Tuesday for a bail hearing on charges he murdered his girlfriend Reeva Steenkamp on Valentine’s Day.