The broadcaster apologised for the disruption and said it was working to ‘restore normal service as soon as possible’.
As presenters Nick Robinson and Martha Kearney tried to host the show an alarm rang, with a message saying: “Please the leave the building immediately.”
Robinson said: “We have a little alarm going on here”, which Kearney said was “quite dramatic”, adding: “Hopefully it is a false alarm”.
The broadcaster then introduced a report on Ghislaine Maxwell while the staff “work out what is going on”.
Shortly after 7.40am an announcer said: “This is BBC Radio 4. I’m afraid we’re having some problems which are preventing us from continuing with our scheduled programme as smoothly as we wish.
“Many apologies for the disruption, but rest assured we are doing our best to restore normal service as soon as possible.”
A second message was broadcast saying Radio 4 was “still suffering some problems and can’t bring you our scheduled programme at the moment”.
Some listeners also experienced issues accessing the programme via the BBC Sounds online app.
The show returned at 7.55am after around 20 minutes, with Kearney declaring: “Alarm over.”
Robinson said: “As far as we can tell there wasn’t actually an emergency. We were outside in the cold for a little while but we are relieved to be back on the Today programme.”
He also tweeted a photo of himself and Kearney back in studio preparing to resume normal service.
The programme continued with Thought For The Day.
A Radio 4 spokesperson said: “Nick explained to listeners that an alarm meant the Today team had to leave the studio disrupting the programme for a short while but it returned to normal as soon as possible.”