Richard, 60, was appearing on the tea-time show to promote Red Nose Day 2017 with comedian Lenny Henry, 58.
The blunder came about as the Vicar of Dibley writer was shown a clip of a man who was also named Richard Curtis.
Forgetting where he was entirely, Richard exclaimed: "Whenever I Google myself that b****** comes up!"
As soon as he uttered the profanity, the studio audience began to laugh and presenters Matt Baker and Michelle Ackerley tried to calm the situation.
Richard Curtis swore live on The One Show tonight
Richard was appearing on the show with Lenny Henry to promote Red Nose Day 2017
It's a family show!
Matt explained: "Family show. It's a family show."
Mortified by what he had just said, Richard apologised, saying: "No swearing! I'm so so sorry!"
Fellow guest Lenny found the whole debacle very funny began to playfully hit Richard over the head.
Luckily the reaction from those at home was one of amusement rather than outrage as viewers took to Twitter to discuss what had happened.
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Matt Baker and Michelle Ackerley attempted to calm the situation after the live gaffe
Mortified, Richard was playfully hit over the head by Lenny
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One person said: "#theoneshow that was hysterical when Richard Curtis lost it ! well held together, I would have corpsed it was just so natural made my day."
Another added: "#theoneshow Richard Curtis calling someone a b****** live on air. Brilliant. #legend."
"Hahaha Richard Curtis dropping swear bombs on #theoneshow – then going beetroot," someone else laughed.
The One Show continues tomorrow night at 7pm on BBC One.