Addressing the Scottish parliament, Sturgeon said the holidays should be viewed as "an opportunity to further limit social interaction".
It comes as ministers in Scotland roll out additional measures to prevent the spread of coronavirus; Scotland recorded 383 new cases on Tuesday (22 September).
"Please think of the October break as an opportunity to further limit social interaction," said Sturgeon.
"And, given that this is a global pandemic, please do not book travel overseas for the October break if it is not essential."
Her comments follow reports the Scottish government was considering a so-called "circuit-breaker" lockdown during the October holidays, which could include travel restrictions.
TTG has approached the Scottish Passenger Agents’ Association for comment.
