The woman in her late 40s was hit by a Toyota Yaris on Maughan Street in Dudley on Thursday at around 5.30pm.
West Midlands Police said the driver stopped at the scene and is assisting with enquiries, but the force said it wants to hear from anyone who might have seen what happened.
A spokesman for West Midlands Police said: "A Dudley woman is in a critical condition in hospital after being hit by a car on Thursday evening.
"We’re asking for anyone who saw what happened or has dash cam footage to contact us to help with our investigation.
"The woman, in her late 40s, was on Maughan Street just after 5.30pm when she was hit by a Toyota Yaris.
"The driver of the car stopped at the scene and is assisting with our enquiries, but we still need to hear from anyone who can tell us what they saw.
"Our Serious Collision Investigation Unit can be contacted by email on FL_COLLISION_INVEST@westmidlands.police.uk or via Live Chat on our website quoting log 3241 of 24/11."