Eurotunnel says plans to introduce exit checks on all people leaving the UK will lead to major cross-Channel delays unless new technology is developed.
From 8 April, immigration officials will record passport details of everyone when they leave the country.
Eurotunnel's John Keefe said the changes were likely to cause tailbacks.
The government said the exit checks were needed to combat illegal immigration and would be introduced with the "least possible disruption".
"On a peak day we might be carrying 10,000 or 12,000 cars. The smallest delay in the journey at any point in the terminal results in an immediate tailback," he said.
"Those tailbacks - cars or trucks - are the kind of thing that can very quickly overflow on to the motorway and if they overflow on to the motorway then we're into a broader problem and we've got the possibility of Operation Stack being brought into place.
"If we can generate a system for the future which is much more automated and uses the advances in technology that have happened over the past few years and are growing apace at the moment then we could find a technological solution to this."
But Mr Keefe added: "It's unlikely the technological solution will be in place by 8 April.
"If trade and tourism is stopped at the border by the border control process, somehow we've missed the point."
When Operation Stack is put in place lorries are parked on the M20 and non-freight traffic diverted off the motorway.
'Checks track terrorists'
A spokeswoman for the Home Office said: "We already collect most of this information automatically in advance, and have been working closely with ports and carriers to ensure checks on remaining routes are introduced properly and with the least possible disruption to customers.
"The data collected will provide the most comprehensive picture we have ever had of whether those who enter the UK leave when they are supposed to.
"It will improve our ability to identify which people have overstayed, take targeted action against those abusing the law and identify and tighten the immigration routes and visas that are most vulnerable to abuse.
"Exit checks will also improve security by helping the police and security services track the movements of known criminals and terrorists."