North Yorkshire Police Roads Policing Group said the BMW driver drove off the A66 near Richmond at around 3am on Tuesday morning (March 2).
Police were called after the orange flashing headlights of the car were spotted by a concerned passerby.
The driver claimed he had swerved for "something" - ending up in the field, police said.
'His efforts to drive it out just bogged it down further prior to our arrival', police added.
In a statement released on social media, the force confirmed the five occupants of the car from County Durham had been given Covid fines after telling police they had been 'visiting Nana'.
However, the five mile expected journey between South Hetton and Peterlee had 'bizarrely extended to 40 miles', police said.
Police said: "Bizarrely the 5 occupants from County Durham had been visiting Nana...the journey of 5 miles between South Hetton and Peterlee had bizarrely extended to 40 miles, encompassing the Richmond area.
"Luckily Nana was safely at home and can await these five returning back complete with Covid fines issued.
Our officers used two Police vehicles to stop the traffic whilst the recovery driver extracted the car from the field.
"All people having to come in one location unnecessarily just because people didnt stay home...."