Babcock, which is building the carriers at its shipyard in Rosyth, revealed he was stepping down with immediate effect following the comments in The Daily Telegraph.
Lord Hesketh was reported in the newspaper saying the Â£5.2 billion carrier project would make Britain a “laughing stock” following defence cuts.
Last month’s defence review revealed only one carrier would operate for three years and never carry planes, while the second would not carry aircraft until at least 2020.
Babcock issued a statement earlier on Monday distancing itself from Lord Hesketh’s comments.
It said: “Babcock dissociates itself from these personal comments, which do not in any respect reflect the views of the company.
“Babcock with its partners in the Carrier Alliance is focused on delivering this major upgrade to the UK’s defence capability on time and to budget.”
Lord Hesketh criticised prime contractor BAE Systems for having a “vested interest” that had caused extra expense.
“We are paying twice as much as we should to get half the capability,” he said.
The carriers will have to be fitted with catapults at extra cost to launch F35 fighter jets, which are being built by BAE and Lockheed Martin, but will not be ready until 2020 while plans for a jump jet version have been scrapped.