The 38-year-old was verbally abused and punched in the face by another man wearing a blue gilet.
Police believe the man responsible for the assault is the woman's friend or partner.
The victim sustained cuts to his face and significant bruises, but did not require hospital treatment.
The assault unfolded at the Jack Hayward Way store just before 2.30pm on December 21.
A spokesman for West Midlands Police said: "We are appealing for information after a man was assaulted after politely asking a woman not to touch items she wasn’t going to buy in Asda, Whitmore Reans.
"As part of our investigation we have released CCTV images of the suspect, and we are asking for your help to identify him."
Anyone with information is urged to call West Midlands Police on 101, quoting crime reference number 20WV/318359H/20.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org