Edmund King said millions of cars rushing out to fill up their tank would “put a strain on the system”.
“Earlier in the week, there were some problems with the supply chain, as we know, due to a shortage of some lorry drivers, but that was only a localised problem,” he told BBC Breakfast.
The AA president said the shortage had been made worse by drivers “going out and filling up when they don’t really need to”.
BP and Esso has been forced to shut some of their petrol stations this week amid a lack of fuel due to a lorry driver shortage.
Concerns over fuel running out of stock has sent drivers to fill up tanks en masse, with reports of increased demand and images of long queues at petrol stations shared online.
“If you think about it, 30 million cars out there, if they’ve all got half a tank [and] if they all rush out to fill up the rest of the tank and the tank is about 60 litres, that will put a strain on the system,” Mr King from the AA told BBC Breakfast on Saturday.
He said the issues were unlikely to last because the supply chain is not being disrupted by ongoing problems such as industrial action.
“The good news is you can only really fill up once – you’ve got to use the fuel, so this should be a short-term thing,” he said.
He predicted the “strain on the system should ease up in the next few days”.
Mr King later tweeted that he had been on the radio “trying to reassure drivers there is no shortage in petrol or diesel at source”
“Please stick to normal filling patterns and this will be temporary blip as new supplies delivered every 24 to 48 hours,” he added.
Earlier this week, EG Group said it was setting a £30 per customer limit for fuel at its forecourts due to supply problems and panic-buying, while Shell said it had also seen increase demand for fuel at some stations.
While fuel shortages are unlikely to last, Mr King said a shortage of lorry and HGV drivers was an ongoing issue.
Hoyer, one of the UK’s largest fuel logistics companies said this week it was struggling to meet deliveries for clients including BP, Esso and Shell due to driver shortages.
Additional reporting by Press Association