The breakfast show host is said to have halted the regular item in the wake of Jacintha Saldanha's death earlier this month.
Nurse Saldanha was found dead in a suspected suicide after transferring the call in which Australian DJs Mel Greig and Michael Christian pretended to be Queen Elizabeth II and Prince Charles to gain medical details about the hospitalised Duchess of Cambridge.
The ban has been enforced as a mark of respect for the nurse's family and colleagues, according to The Mirror.
The 'Call or Delete' segment involves celebrity guests looking through their mobile phone contacts and selecting a random number, before choosing whether to prank call them or delete the number.
A BBC spokesperson said: "Despite rigorous editorial procedures around the use of hoax calls on air, given recent events we have decided to suspend the Call or Delete feature for the time being."
The feature is expected to return in 2013.
Professor Green recently pranked his girlfriend Millie Mackintosh on the show, by pretending that he had an affair with Imogen Thomas.