John Marovic and Johnny Kresimir, owners of Johnny's Booze and Pool, said they received a notice in the mail telling them they have until Tuesday to remove the sign or face a $940 fine, but they plan to fight the order, KCBS-TV, Los Angeles, reported Wednesday.
The city said the sign posted above the bar, which reads "Thank a veteran for your freedom," violates the local signage ordinance.
Veterans said they appreciate the sign.
"I love this place. The sign gives me the pride back that I lost... I struggled a lot when I first came back," said an Army veteran whose name was not reported.
"I can understand city ordinances, but it's been up there for 10 years. I don't understand why it's a problem now," another veteran said.
Matthew Harper, the city's pro-tem mayor, said he would support granting a variance to allow the sign to remain in place and he has contacted the city manager's office about the issue, the newspaper said.