Her disappearance has been described as “very out of character”.
A man has been arrested in connection with the investigation and currently remains in custody.
The launch of the investigation comes after police said they were “seriously concerned” about Sarah’s whereabouts on Saturday.
In a statement, they said: “A murder investigation is underway following the disappearance of Sarah Henshaw from Ilkeston.
“Sarah was last seen at around 9pm on Tuesday 20 June at her home address on Norman Street, Ilkeston and has not been seen since.”
They added: “The 31-year-old is described as white, of a medium build with long dark straight hair which she wears in a bun.
“She is thought to be wearing a black lightweight coat, a khaki green top, blue skinny jeans, and black flat pumps. She also has a tattoo on her right foot.
“A man has been arrested in connection with the investigation and remains in custody.”
The police said they were “keen to hear from anyone that may have CCTV or dashcam footage of a blue Ford Transit van in the early hours of Wednesday 21 June around the area of J29 of the M1 and the A617 Chesterfield”.
Detective Inspector Maria Pleace said: “We have information in relation to Sarah’s disappearance that has led us to believe that she may be seriously hurt or deceased.
“Sarah’s disappearance is very out of character and finding her is our number one priority at this time.
“I would like to appeal to the public for CCTV and dashcam footage as stated or any other information that may be of use to our investigation.”
Derbyshire Police added: “Anyone who has any information that may assist our investigation is asked to contact us using the methods below and quoting incident number 444 of 23 June.”
They said people can “also anonymously contact the independent charity CrimeStoppers, on 0800 555 111, or by visiting the CrimeStoppers website”.
