The plea comes amid a surge in congestion outside the Harvest Energy petrol station in Grange Road, Gosport.
Queues outside the station have become so bad, vehicles are being diverted away from the area in a bid to ease the traffic.
In a statement on Facebook, Hampshire police said: ‘We are currently dealing with a lot of queuing traffic outside the Harvest Energy Petrol Station on Grange Road in Gosport.
‘If you really don’t need fuel, please avoid the area if possible, vehicles are currently being diverted down Military Road to avoid the area.’
Man dies after dog attack at Hillson Drive recreation ground in Fareham - owner is arrested
Fareham dog attack: Shrine set up in memory of man who died - named locally as Wiggy Symes
Heartfelt tributes paid to Wiggy Symes who died after Fareham dog attack
Thunderstorms yellow weather warning issued over Waterlooville, Fareham and parts of Hampshire by Met Office with chance of 'heavy rain'
Seven - including five teenagers - arrested after Lower Drayton Lane burglary in Portsmouth
Traffic also came to a standstill along Newgate Lane in Fareham on Sunday as drivers queued to get into Asda.
The situation comes amid a warning from fuel industry bosses, who last night said the petrol crisis in the south east was ‘getting worse’.
Tomorrow will see military drivers from the army being drafted in to help deliver fuel to stations across the nation, after NHS staff and key workers were caught up in queuing that has persisted for days.
Health secretary, Sajid Javid, has attempted to calm concerns over the weekend insisting the woes around petrol were ‘stabilising’ in most parts of the country and that military involvement was just a precaution.
However, Brian Madderson, the chairman of the Petrol Retailers Association, said it remains a ‘really big problem’ in some areas.
‘In London and the south-east, and possibly parts of eastern England, if anything it has got worse,’ he told the BBC’s Today programme. ‘[The use of the military] isn’t going to be the major panacea.
‘It’s a large help but in terms of the volume, they are not going to be able to carry that much.
‘Expect anything from 1, 2 or even 3p a litre increases at the pump. This is not profiteering. This is genuine wholesale price increases causes by global factors.’
The queueing outside stations has already affected bus services across the Portsmouth area.
First Bus has been forced to re-route several services across Fareham and Gosport to avoid the congestion during the day.
The travel operator is providing regular updates on its service changes via its Twitter.
Taking to social media. First Bus added: ‘Due to Grange Road being heavily congested with cars waiting for fuel, we are going to divert to Fareham only via Military Road, Rowner Road & Grange Road and then back onto normal route.’