The ordinance would require ice cream trucks to turn off their music when they are serving customers, the Los Angeles Times reported Thursday.
Council members said they have been getting a lot of flak for the proposed regulation.
"I want to state for the record, I do like ice cream and I enjoy ice cream trucks," Councilman Dee Andrews said. "We just have to strike a balance of the needs of our neighbors for peace and quiet and the business needs to sell ice cream."
Ice cream vendors say they are worried the ordinance will have a negative impact on their business.
"The music is what brings the children out. If they take that away, our businesses are going to be affected in a negative way," said vendor Ismael Hernandez, who has peddled ice cream in Long Beach for 13 years. "The music is vital for us."
Long Beach residents who live near parks frequented by ice cream trucks say the music -- which often includes songs such as "La Cucaracha" and "It's a Small World" -- can be annoying.
"Sometimes I'm trying to watch TV and as much as you try to ignore the music, you can't," said Isaura Lopez, 23, who lives near MacArthur Park in Long Beach.