Relatives were visiting a floral memorial for Kulvinder Kaur in Cavendish Road, Beechdale, on Saturday, just two days after her death.
But family members who had returned to the scene of the crash to pay their respects where confronted with vile comments from a passer-by.
Officers investigating the "deplorable" crime have identified and interviewed the suspect and are asking for the help of members of the public who also heard the abuse.
Sergeant Stephen Pursglove, from Walsall Police, said: "Racial abuse is unacceptable at any time, but feels even more despicable when a family have just lost a loved one.
"The abuser was on foot so we believed he was local and most likely aware of what tragically happened just two days beforehand.
"This makes it all more deplorable and we are urging anyone who can help our investigation to get in touch as soon as possible."
Mrs Kaur was hit by a Peugeot 206 in Cavendish Road just after 1pm on September 12 and the 52-year-old was pronounced dead at the scene.
Anyone with information is asked to contact police via Live Chat at west-midlands.pnn.police.uk between 8am and midnight or call 101 anytime. Quote crime reference number 20WS/218651X/19.