Natalie Hemming, 31, from Milton Keynes, was was last seen in Hemel Hempstead at around 4pm on Sunday.
There have been no known sightings of her since then.
A 42-year-old man from Milton Keynes was arrested yesterday on suspicion of murder and is currently in custody.
Head of major crime, Det Supt Chris Ward, said a vehicle believed to have been driven around Aylesbury on Bank Holiday Monday could hold vital clues about Natalie’s whereabouts and appealed for anyone who saw it to contact them.
He said: “The vehicle is a Black Ford S-Max Titan X Sport, registration EJ12UWG.
“We believe the vehicle travelled on the A413, the A418 and the A41 around Aylesbury, between 9.45pm on Sunday and 00.45am on Bank Holiday Monday.
“If anyone saw this vehicle in this time period, either travelling or pulled over somewhere, please contact police as soon as possible.
“Any detail, no matter how insignificant you think it is, could help with this investigation and help to locate Natalie and return her to her family.
Det Supt Ward added: “We are increasingly concerned about Natalie. Her disappearance is out of character and she has not contacted her family or been in touch to check the welfare of her children since she has been missing.
“She made no preparations to go away and she did not arrive at work on Tuesday.
“We are keeping an open mind about the circumstances of Natalie’s disappearance and our priority continues to be finding Natalie and returning her safely to her family.
“I would like to hear from anyone who has seen or heard from Natalie.
“Natalie has three children and a family who are desperate to hear that their mother is safe. Officers are keeping her relatives updated and supporting them through this difficult time.
“I would urge anyone who has any information about Natalie, or the black Ford car, to contact police as soon as possible, quoting reference number 1478 (4/5).
“If you don’t want to speak directly to police, you can contact the independent charity Crimestoppers (opens new window) anonymously on 0800 555 111. No personal details are taken, information is not traced or recorded and you will not go to court.”
Natalie is white, approximately 5ft 1ins, of slim build, with shoulder length brown hair and blue eyes.