The Deputy First Minister said travel was only permitted for essential reasons as international travel restrictions ease across Scotland with the exception of Glasgow and Moray.
Scotland has now moved to the traffic light system for international travel, with those returning from green list countries required to take a coronavirus test while avoiding the 10-day quarantine period.
On Monday, May 24, the first direct international flight from Scotland since the rules were relaxed set off for Portugal (Faro) via Ryanair from Edinburgh Airport at around 6.10am.
A flight from Faro to Edinburgh Airport is also expected to land at around 12.50 am on Monday.
Speaking about the new rules on the BBC’s Good Morning Scotland programme, Mr Swinney said people must exercise ‘due caution’, however added that people have to make their choices.
He said: “There are obviously many reasons why individuals have to travel, not all of it is about going on holiday, there can be essential family connections that people wish to pursue.”
He continued: “We’re trying to create pathways for essential travel but our advice to people is that they should observe that essential travel element, that we should not be undertaking non-essential travel at this particular time.”
Asked about the fact many flights to popular holiday destinations are resuming, the Deputy First Minister added: “People have got to make their choices, we do live in a free society and we are trying to enable people to get back to some form of normality after a period of severe constraint.
“But we are appealing to people, given the fragility of the situation we are in, to exercise due caution and to take steps which will minimise the risk of any circulation of the virus and to minimise travel that is not absolutely essential in the coming period.”
Nicola Sturgeon announced an easing of international travel restrictions earlier this month.
From Monday, the Scottish Government is also imposing temporary restrictions on travel to three areas in England which are dealing with outbreaks.
These are Bedford, Bolton and Blackburn with Darwen.