Madison Wright, 30, from Basildon in Essex, was wearing a pink top, black trousers and flip-flops when she was last seen alive on July 22.
His car, a black Vauxhall Astra with registration number EU13 JVW, was found four days later, on July 26, in Basildon.
Essex Police said a 36-year-old man from Pitsea was arrested on Friday morning on suspicion of the murder of Ms Wright.
Ms Wright is understood to know the suspect, who remains in custody.
Madison Wright, 30, from Basildon in Essex, was wearing a pink top, black trousers and flip-flops when she was last seen alive on July 22.
Ms. Wright, who is 5 feet 8 inches tall, slim, has hazel eyes and shoulder-length blonde hair, has not been seen or heard from since 8:30 a.m. on Friday, July 22.
He has a tattoo of a dream catcher on his left arm and a tattoo of a rose on his right hand.
Detective Superintendent Rob Kirby, of the Kent and Essex Serious Crime Directorate, said: “Madison is a young mother, with a family who love her and are desperately worried about her.
‘She has been missing for a week today and she is still missing, and we desperately need to find her.
“We have a dedicated and specialized team of officers and staff working to find her and we urgently need anyone with information about her disappearance to contact us.”
His car, a black Vauxhall Astra with registration number EU13 JVW, was found four days later, on July 26, on Brackendale Avenue in Basildon.
He said officers want to speak to anyone who may have seen or heard Ms. Wright since the morning of July 22, or saw her between then and when her car was found on Tuesday, July 26.
The force is also requesting CCTV, dash cam or other footage in connection with the incident.
Essex Police have set up a dedicated phone line for people to give them information on 0207 1267612.
