They struck at the cemetery on Jeffcock Road earlier this week and made off with over 50 of the bronze plaques, each measuring 24 inches by 18 inches.
The incident has been reported to West Midlands Police and anyone with information is asked to please call 101 and quote crime reference number 20/639096/22.
Councillor Steve Evans, the City of Wolverhampton Council's Cabinet Member for City Environment and Climate Change, said: "This is an absolutely deplorable act which we condemn in the strongest possible terms.
"It will no doubt sicken the families of those affected, and we are determined to do all we can to help track down the culprits.
"The incident happened during the night and Merridale Cemetery was locked at the time, so we think those responsible must have either scaled the entrance gates or cemetery walls in order to gain access.
"I would ask anyone who has any information which may help apprehend the culprits to contact police on 101 as soon as possible."
Chief Superintendent Richard Fisher, of Wolverhampton Police, said: "We recognise the devastating effects crimes such as these have on grieving family members.
"We are making enquiries to seek to identify the culprits and ask for all our metal recycling and scrap merchants to help us by not accepting any items they are likely to be part of this theft and call us should anyone attend trying to dispose of them. We will be passing the message during visits to our local dealers."
