The presenter, 94, has been on the BBC Radio 4 programme since its inception in 1967 but was absent from Monday night's instalment.
Gyles Brandreth filled in for him, prompting an outpouring of worried messages from fans on social media.
The BBC's head of radio comedy Julia McKenzie was quick to assure listeners that Parsons was just enjoying a rare day off.
She tweeted: "Just to reassure those listening to the very unexpected Just a Minute on @BBCRadio4 at the moment - the apocalypse is not upon us - @GylesB1 kindly stepped in to give Nicholas Parsons a couple of days off.
"NP is totally fine and is still the guvnor as per the last 50 years."
However, plenty of people still wrote messages online saying that Just A Minute without Parsons felt like the end of the world.
One said: "The latest sign of the impending apocalypse. Nicholas Parsons is not in the chair for #justaminute."
Another person posted: "Omg what happening. Nicholas Parsons isn't presenting #justaminute. End of days. @BBCRadio4."
"Somewhere, the captain of a nuclear submarine is trying to work out what it means when Nicholas Parsons isn't hosting #justaminute," said another.
One person suggested it was like "the ravens leaving the Tower of London".
McKenzie responded to some of the comments, assuring fans: "He's totally fine - we thought we'd allow him a day off after 50 yrs!"
She replied to another message by saying: "Yes don't worry he is fine and well - just a day off!"
Another tweet read: "NP is totally fine just taken a couple of days off - he's a 50 year perfect attendance record so we thought that was probably ok."