SNP’s Europe spokesperson, Dr Philippa Whitford, has cited a “disastrous hard Brexit” for the costs.
British travellers are set to be charged €7 [around £6] to visit any of the 26 European countries within the Schengen zone from November next year.
The visa fee for UK passport holders was due to be introduced in May 2023, but the European Commission has postponed it by six months.
British tourists will not need a visa for short stays in the EU up to 90 days, but are expected to have to apply to the European Travel Information and Authorisation System (ETIAS) for a visa waiver.
The SNP has claimed an ETIAS application could take up to 30 days to process.
Dr Whitford said of the new fee: “Add this to the health insurance costs and the roaming charges British travellers are already facing following the Tories' disastrous hard Brexit, and it all adds up to make things unnecessarily expensive.
"The Westminster Government's Brexit obsession is not just hindering people's ability to holiday abroad, but also heaping further costs onto touring performers trying to make a living in the middle of a cost-of-living crisis and businesses that are already struggling to keep up with energy bills, given they are not subject to the energy cap.
“Another consequence of Brexit, which Scotland didn't vote for, is the huge administrative delays that are wreaking havoc on peoples' plans, such as the Passport Office chaos that has been ruining family holidays for months now.
"Far from opening the UK up to the world and shedding layers of bureaucracy, the Tories have effectively shut the UK off from our closest neighbours and allies with their misguided ideology.
“Whatever way you look at it, Brexit has been a complete disaster – a political choice that has stripped away people's freedom of movement and added serious economic harm to the UK.”
The move comes as a result of Brexit negotiations between the UK and the EU following the vote to leave the European Union back in 2016.
The UK Government has been contacted for comment.