Police are urgently trying to arrest a male suspect after the women, aged 49 and 22, were killed in Solihull on Monday.
Officers were called just after 12.30am and the pair were pronounced dead at the scene on Northdown Road.
Detective Inspector Caroline Corfield appealed to the suspect to come forward.
She said: “We are still in the very early stages of our investigation but we believe the offender is known to the victims.
“We are appealing to him to come forward as a matter of urgency.”
She described the deaths as “truly devastating and heart-breaking”.
The area has been cordoned off and house-to-house inquiries are being carried out.
CCTV footage is being examined, West Midlands Police said, adding that there will be a visible presence in the area in the coming days.