Radio 4's Special Correspondent, who is 64, had a heated exchange with outspoken conservative pundit Ann Coulter, which saw him branded him with the unusual term of endearment.
It is usually used to refer to one's partner or crush.
Naughtie admitted the interview was not "normal" in the sense that "you can't really get a word in edgeways when you're talking to somebody like that".
The remark prompted John Humphrys to quip: "Sounds a bit like Boris Johnson."
Naughtie continued, recalling: "Well she did call me at one point in the interview 'babycakes', which is the first time that's happened to me."
After the heated discussion, fellow presenter Mishal Husain brought proceedings back to the studio saying: "Jim 'Babycakes' Naughtie reporting from the US presidential campaign trail."
During their tense exchange, Naughtie quizzed Coulter on whether it would be acceptable for a leader to make comments similar to Trumps 'ban Muslims' remarks about Jewish people immigrating to New York at the turn of the twentieth century.
Coulter replied: "That's like 2% of the population. That did not overwhelm our culture. Yeah we take immigrants but we have pauses once in a while - we're being overwhelmed."
She admitted that immigration was "100%" the central issue of Trump's campaign, and added the Republican presidential candidate was right on foreign police with Mexico.
"They have been sending rapists and drug dealers," she said. Coulter added that the US' border with Mexico had "wrecked lives, wrecked communities, wrecked states."
According to Pew Research Center, Muslims make up about 1% of the US population. It estimates it will reach 2% by 2050.