A back-up generator supply has been used to maintain lighting since November when faults caused the lights to fail.
The car park will be closed for around 24 hours from 6pm on Sunday, 29 January continuing late into the evening of Monday 30 January.
Undertaking the work, Selby District Council says the whole car park is required to be closed throughout due to health and safety considerations.
Meanwhile, a legal dispute between the council and local brewers, Samual Smith's Old Brewery, is now set to add further delays to plans to remodel the car park.
Planners had granted permission for the council to update the car park in April 2011, planning to improve access and resurface the car park with Tarmacadam.
But the brewery applied for a Judicial Review of the decision, the outcome of which is now awaited before it is known whether the work can take place.
The lighting problems, however, are being dealt with separately, as these are emergency repairs to existing facilities on site.
A spokesman for the Council said, "The car park will be closed to carry out emergency repairs to the lighting, but because of the current legal action surrounding our plans for the car park we won't be able to make the other improvements we think are necessary. We're only able to make the minimum of repairs at this stage."
Alternative car parking will be available at the nearby Britannia car park whilst the works take place.

