Johan Lundgren told Sky News that a planned traffic light system for destinations, which will demand pre-departure and post-arrival COVID-19 tests for passengers, would pile costs on travellers.
The measures were outlined on Monday as the government works towards a planned restart for holidays from 17 May, under the PM's roadmap for England.
However, Boris Johnson was only able to tell reporters that he hoped that would be the case, as a review was ongoing.
There remain real concerns that with a third wave of infections in Europe a push to resume holidays could import cases and new variants.
Under the planned traffic light system, assessments on where is deemed safe will be based on a range of factors, including the proportion of a country's population to have been vaccinated.
While those returning from countries rated "green" will not be required to self-isolate, coronavirus tests will still be needed before leaving and on arrival.
The recommended PCR tests would cost up to £200 per person.
Test results may yet fall into a so-called vaccine passport regime, which is still being considered for trips both abroad and even at home.
The government's advice is that no one should be booking foreign travel just yet, despite operators reporting a surge in demand following a year of misery for the sector that has cost tens of thousands of jobs.
Mr Lundgren told Ian King Live he remained hopeful of a strong summer ahead, if measures to control the spread of coronavirus allowed, and was confident of more details soon on a restart from 17 May.
But he said of the planned traffic light system: "If you are categorised as a 'green country'... there should be no restrictions at all really because what I'm afraid about is that if the government are now adding cost complexity, even if you are in the 'green' bucket, that's going to make it out of reach for many families if you look at what the cost would be.
"If, for instance, you needed to do a PCR test you wouldn't open up international travel for everyone, you would open up for those who can afford to pay that."
Rory Boland, Editor of Which? Travel, responded: "Testing will be essential for restarting travel safely, but private tests in the UK are currently too expensive and risk pricing most people out of travel.
"Other countries have found solutions to reduce the cost of private testing, so if the government is serious about making travel safe and affordable when it restarts, it must urgently look at ways to reduce these expenses."
There was general disappointment across the industry that the PM could not give greater certainty over the reopening date and rules.
Heathrow chief executive John Holland-Kaye said: "Now that a safe, scientifically-backed process has been agreed upon, a clearer timeline for the return to international travel is needed."