Barnsdale Road, in the east Leeds village of Allerton Bywater, near Castelford, has closed after the River Aire flooded.
The Environment Agency said the spillway at Allerton Ings is operating but the washlands are filling and it expects the spillway to continue until Thursday, January 21.
It comes as an amber weather warning for rain was put in place by the Met Office as Storm Christoph looks set to batter the city.
Sergeant Micklethwaite, of West Yorkshire Police, reported that drivers have ignored the road closure signs and become stranded on the road.
Sgt Micklethwaite said: "Please DO NOT ignore the signage on Barnsdale Road. We have had to assist stranded motorists already."
North Yorkshire Fire & Rescue Service also reported that they have received calls about stranded cars.
The service shared a warning on its social media channels, which read: "We are starting to receive a number of calls across the county where cars have driven into floodwater.......PLEASE DO NOT DRIVE INTO FLOODWATER."
Earlier in the day, the Leeds District team from West Yorkshire Fire and Rescue Service said: "Rainy day reminder that if there's water on the road that looks above ankle deep - don't risk driving through it.
"Turn around and find an alternative route, it may take longer in the short term but it'll save you loads of potential hassle.
"The same goes for road closures - the chances are that if a road is closed then it's closed for a very good reason."
West Yorkshire Prepared is the Local Resilience Forum for West Yorkshire which is made up of the region's key emergency responders and specific supporting agencies.
The Partnership works to help communities prepare for, respond to and recover from emergencies and major incidents.
It has issued vital flooding advice and guidance today for the region as Storm Christoph hits.
Areas which are under a flood 'alert' should prepare by:
- Packing medicine and insurance documents
- Visiting the flood warning information service
These are the areas at risk of flooding in Leeds.
Areas which are under a flood 'warning' should act by:
- Moving things upstairs or to safety
- Turn off gas, water and electricity
- Move family, pets and car to safety
These are all the locations of flood warnings in Yorkshire.
Areas which are under a 'severe' flood warning should survive by:
- Following emergency services' advice
- Call 999 if in immediate danger
- Staying safe