The insult popped up at the bottom of the screen during a tennis update.
Later in the morning, a presenter apologised to any United fans who may have been offended.
She said the mistake had occurred as someone was learning how to operate the ticker and was "writing random things not in earnest".
The presenter said: "A little earlier, some of you may have noticed something pretty unusual on the ticker that runs along the bottom of the screen with news making a comment about Manchester United, and I hope that Manchester United fans weren't offended by it.
"Let me just explain what was happening -- behind the scenes someone was training to learn how to use the ticker and to put text on the ticker, so they were just writing random things not in earnest and that comment appeared.
"So apologies if you saw that and you were offended and you're a fan of Manchester United."
A BBC statement to the PA news agency said: "There was a technical glitch during training with our test ticker, which rolled over to live programming for a few seconds. We apologised for any offence caused on air."
BBC presenter and Manchester City fan Clive Myrie tweeted: "I had nothing to do with this!!" with the hashtag #mcfc.
Manchester United, who have not won silverware since 2017, finished sixth in the top-flight table with their lowest points tally of the Premier League era.
Their new manager, Erik ten Hag, was formally unveiled on Monday, less than 24 hours after Manchester City clinched a fourth league title in five seasons.
Manchester City's players attend an event for fans with members of the Manchester City football team following an open-top bus parade through Manchester, north-west England on Monday, to celebrate winning the 2021-22 Premier League title.