Maureen Bannister, 43, from Leuchars, has not been seen since about 14:00 on Sunday.
It is understood that shortly after this Ms Bannister left a house on Pitcairn Park in a blue-coloured Ford Focus with her dog, a black/grey-coloured cross-breed Yorkshire Terrier.
Ms Bannister is known to walk her dog in and around Tentsmuir Forest.
The dog was found near the woman's car in the Tayport area shortly after Ms Bannister was reported missing.
The missing woman was described as 5ft 4in tall, of slim build and has long dark hair.
It is not known what she was wearing at the time of her disappearance but it is likely she will have been wearing navy Wellington boots and a navy thigh-length jacket with a cream-lined hood.
Insp Paul Dick, of Police Scotland, said: "Our search for Maureen has been under way since around 01:00 on Monday but unfortunately we have not yet located her.
"We are extremely concerned for her welfare as are her family who are desperate to find her safe and well.
"Today, I'm appealing to anyone who may have seen Maureen or even spoke with her, to come forward to police immediately."
A police helicopter and dogs are searching for a missing woman in Fife.