A number of road closures are still in place after the River Don broke its banks in several places earlier this week.
But there have been numerous reports of drivers ignoring signs and barriers put in place.
A spokesman said: “We are receiving reports from partners such as Doncaster Council of motorists ignoring road closures put in place for flooding and continuing down carriageways.
“In doing so they are risking themselves, any passengers they may be carrying, their vehicles and the safety of those who may have to come and rescue them if they get stranded.
“Please drive carefully and don't do this!”
On Tuesday, a Doncaster Council spokesman said: “Please do not remove flood road closure signs or barriers or attempt to drive through road closures or flood water.”