Bin collections across the North East Lincolnshire will be unaffected by the panic buying of petrol, the council said.
Local authorities in other part of the country have been forced to cancel some waste collections due to the demand for fuel.
Petrol forecourts across Grimsby and Cleethorpes have seen long queues this week despite calls for calm.
However, North East Lincolnshire Council has confirmed that all bin collections will be made as normal.
Residents should continue to put bins out on the usual days.
The crisis is continuing into its fifth day with more petrol stations running dry.
There have been calls to prioritise fuel for care workers to ensure that emergency and healthcare services are able to continue doing their job.
The government has temporarily suspended the competition laws to allow the industry to share information on which areas are running low.
The panic was sparked by a leak from BP which revealed that there was a shortage of lorry drivers to deliver petrol.
The Petrol Retailers Association warned that as many as two thirds of its membership of nearly 5,500 independent outlets were out of fuel on Sunday, with the rest of them “partly dry and running out soon”.
Shell, ExxonMobile and other industry bodies have reassured motorists that there is no national shortage of fuel, and that pressures were linked to “temporary spikes in customer demand”.
Prime Minister Boris Johnson is understood to be considering whether to bring in the army as an emergency measure to deliver fuel.
Dr Chaand Nagpaul, chair of council at the BMA, said: “Emergency and essential workers rely on fuel both to travel to work and for their work itself – whether this is to get to hospitals, practices and other healthcare settings, or for ambulances to reach people in urgent need of care and GPs to visit very ill patients at home.
“Everyone will have their own reasons for needing to fill up, but as pumps run dry there is a real risk that NHS staff won’t be able to do their jobs and provide vital services and care to people who urgently need it.”