Seqirus, one of the world’s largest flu vaccine companies, said it had told customers about delays of up to a fortnight.
The company said it was “working hard to resolve the delay”.
NHS England says patients who are affected will be contacted by their GP.
Seqirus, which supplies vaccines to GP practices and pharmacies in England and Wales, said: “Due to unforeseen challenges linked with road freight delays, we have informed all our customers of a consequent delay to their scheduled vaccine delivery by a maximum of one to two weeks.
The company, which is one of a number of suppliers, said customers would be able to reschedule their flu vaccination clinics.
The professional body representing GPs said it would hit practices.
This is news we really didn’t want to hear”, said Dr Gary How sam, vice chairman of the Royal College of GPs.
“With more than 36 million people eligible for the flu vaccine on the NHS this year, GPs need the supply chain to run like clockwork.
Dr Howsam said GPs are “already under enormous pressure and still waiting for details of how the Covid booster campaign will align with everything else they need to do this winter”.
Doctors meticulously plan jabs each year, he said, adding that it is “essential that as many people as possible in at-risk groups get their vaccination as early into the flu season as possible”.
“A delay of even a couple of weeks is going to have a big impact on practices and their patients, especially when GPs are already dealing with the fallout caused by the shortage of blood test bottles and the anxiety this is causing.”
“General practice and the entire NHS is dependent on the smooth roll-out of the winter flu vaccination programme. It cannot fail,” he said.