Drivers are urged to use caution because visibility was expected to be a quarter-mile or less, making for driving hazardous, the weather service said.
"Slow down," it added. "Use your low-beam headlights ... and leave plenty of distance ahead of you in case a sudden stop is needed."
Rain is likely into the overnight hours as well, with a low of about 34 degrees.
After the fog clears on Thursday, the weather will turn mostly sunny, with a high near 46 degrees for the last day of the year.
By New Year's Eve, it will be partly cloudy, with a low dropping to about 26 degrees.
New Year's Day will be mostly sunny, with a high near 41 degrees and wind chills of 25 to 35 degrees.
Click here to follow Daily Voice Bridgeport and receive free news updates.