The show was forced to move to pre-recorded content after an alarm sounded, telling those in the building to “leave the building immediately”.
A message was played to listeners, saying: "I'm afraid we're having some problems which are preventing us from continuing with our scheduled programming as smoothly as we wish.
"Many apologies for the disruption, but rest assured we're doing our best to restore normal service as soon as possible."
The outage did not appear to affect other BBC radio channels.
Social media users were quick to voice their concern, with some pointing out that the broadcast of the Today programme is allegedly used as a sign by British nuclear submarines of whether the UK still exists.
One said: “Somewhere at sea a nuclear sub is wondering whether to open their sealed orders.”
Another added: “Can someone tell the nuclear subs we’re not at war as this is one of the signs they look for!”
The programme quickly resumed normal service, with Robinson writing on Twitter: “Well that was interesting. Emergency over. If there was one …we’re now back in the studio.”
He added: “As you were. We’re back on air. Normal service has been resumed. Thanks for thoughtful messages.”
A BBC 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.”