Natalie Hemming, 31, of Alderney Avenue, Newton Leys, was reported missing on Tuesday.
The man, 42, and also from Milton Keynes, was arrested by Thames Valley Police earlier in connection with the investigation and is in custody.
Police said Ms Hemming's disappearance was "out of character" and they are still trying to locate her.
Det Ch Insp Simon Steel said officers were "keeping an open mind" about the circumstances surrounding the disappearance.
"Our priority is to find Natalie and return her to her family as soon as possible. We would like to speak to anyone who has any information about where Natalie may be or anyone who has seen her since 3pm on Sunday.
"If you recognise someone fitting Natalie's description or have any details which could assist with the investigation, no matter how insignificant you feel they may be, please contact police."
Ms Hemming is described as white,  about 5ft 3in (1.6m) tall, of slim build, has shoulder length brown hair and blue eyes.
She was last seen on Sunday at 15:00 BST in Hemel Hempstead, Hertfordshire, and was wearing a blue top, blue jeans and a short black jacket.

Scarborough Athletic FC played in its home town for the first time since the club was founded in 2007.
The team, formed after the collapse of Scarborough FC, has been playing home fixtures nearly 20 miles away in Bridlington.
The Sea Dogs lost 4-1 against Sheffield United XI in front of a sell-out 2,000 crowd at Flamingo Land Stadium.
Chairman Trevor Bull said: "Today is not only a great day for our club, it is also a massive day for our town."
The club was formed after Scarborough FC went out of business with debts of £2.5m. It is jointly owned by about 350 supporters.
Fan and club communications officer Will Baines said: "A lot of people have put a lot of work in to the club while we've been in exile, but now we're coming home."
Mr Baines said the move back to Scarborough was key to the future success of the side.
"We're fan-owned which means we've got our destiny in our own hands," he said.
"We've not got a big investor backing us, so that's why it's important that we're back in town as it's the money that we get through the turnstiles every week that will pay for the club."
The homecoming fixture generated such interest the council and club warned people not to congregate on the hill overlooking the ground as it has no public right of way.
The stadium forms part of a £50m development built on the town's former Weaponness Park and Ride site, which includes a swimming pool, new University Technical College and Coventry University's Scarborough campus.
Scarborough FC's former ground - the McCain Stadium -  was demolished in 2011.

PC James Burns was found not guilty of common assault and two counts of assault causing actual bodily harm against Michael Stanley, 28, in Penrhyndeudraeth, on 10 April 2016.
He was also cleared of giving a false statement about what happened.
He had denied all the charges at Caernarfon Crown Court.
The case against another officer, PC Robin Humphreys, who had been accused of perverting the course of justice, was thrown out earlier in the month.
Judge Huw Rees said there was insufficient evidence to prove he had colluded with PC Burns by giving false statements about the incident.
A man has been arrested on suspicion of murder by police searching for a missing woman.
[NEXT_CONCEPT]
A football team has played its first home game in more than 10 years after moving into a new stadium.
[NEXT_CONCEPT]
A police officer has been cleared of assaulting a handcuffed man with pepper spray after arresting him in Gwynedd.