Zobaidah Salangy, 28, was last seen at her home address in the Charford area, of Bromsgrove, on Sunday March 29.
She told her family she was going for a jog but has not returned home or been in contact since.
A 42-year-old man has now been arrested on suspicion of murder in connection with the woman's disappearance and remains in police custody this morning.
Ms Salangy is known to have links to the Birmingham, Smethwick and Walsall areas and was last seen wearing a green parka style coat with a fur hood.
She is described as 5ft tall and of Afghanistan heritage.
A spokesman from West Mercia Police said: "The investigation is still on going and West Mercia Police are appealing for any information."
Anyone with information can call West Mercia Police on 101, quoting incident number 0521S of April 4.
Alternatively, call Crimestoppers anonymously on 0800 555111.