Sergeant Dave Purcell - of West Yorkshire Police - tweeted the warning on Saturday.
Carters Lane in Ilkley has been left covered in sheet ice due to a burst water main.
One police car and one member of the public's car have been rescued so far.
Sgt Purcell said: "Please avoid Carters Lane at #Ilkley - burst water main has caused sheet ice.
"Road is impassible.
"One police car and one member of the public's car already rescued!"
Motorists have been warned of the risk of icy patches forming quickly after sunset following collisions on New Year’s Eve and New Year’s Day.
Met Office meteorologist Alex Burkill said the UK will see “harsh frosts” throughout the first week of January.
“Obviously it’s very cold and it’s going to stay cold through this week,” he said.
“Whilst there will be some wintry hazards around, it’s not really until the end of the week until we see any significant snow.
“I expect it won’t take very long at all for the risk of icy patches to start forming an hour or so after sunset.”
Next week, cold easterly winds will develop, bringing wintry showers, particularly around eastern parts, while hazardous freezing fog, frost and ice risks will all continue, the Met Office added.
RAC Breakdown spokesman Simon Williams said: “The message for those who have to drive is to adjust their speed according to the conditions and leave extra stopping distance so 2021 doesn’t begin with an unwelcome bump and an insurance claim.
“Snow and ice are by far the toughest driving conditions, so if they can be avoided that’s probably the best policy.”
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