Ali G: "Aware of content guidelines"
Talking to DJ Sara Cox on the station's breakfast show, Ali G's language was so strong that fellow guest Shaggy said: "I hope to God my mum isn't listening."
The spokesman for BBC Radio 1 said: "We are very sorry for any offence caused to our listeners.
"It is not something we take lightly.
"Everybody who come on to our shows is made aware of our content guidelines."
The station's audience includes many under-15s - particularly during the school half-term, which for most UK children started on Monday.
Ali G, in real life comedian Sacha Baron Cohen, is currently hoping to hit the charts with the track Julie recorded with Shaggy.
The record has already been censored in order to gain airplay.
In the interview with Sara Cox, Ali G used a four-letter word when describing the removal of offensive language from his new record.
He then joked that he had smuggled drugs from Jamaica in his body, and referred in colloquial terms to having been intimate with singer J-Lo.
Complaints
He went on to describe Pop Idol contestant Gareth Gates as "spasticated", and called the TV show's winner Will Young a "batty boy".
Sara Cox apologised to listeners after Ali G's outburst, and again after the show.
By Monday afternoon the BBC had received 20 calls of complaint about the incident.
The BBC spokesman said: "The producers and everyone involved will have to sit down and see how this came about, and how it can be avoided in future."