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.
Ohio bar shooting arrested, charged with murder
LGBT community has 'bullied the American people': Bachmann