The moratorium covers the 500,000 people living in the 32-square mile area of South Los Angeles, which is predominantly Hispanic and African-American.
Designed to encourage healthier eating habits, the move is believed to be the first time fast-food outlets have been restricted from opening on health grounds.
A spokeswoman for the law's sponsor, Los Angeles City councilor Jan Perry, said the law was approved 12-0 during a hearing on Tuesday that was interrupted by a 5.4 magnitude earthquake that hit the region.
Under California law, fast-food restaurants are defined as establishments which have a limited menu, sell items prepared in advance or heated quickly, have no table orders and serve food in disposable packaging.
Perry described the ordinance's approval as a "victory for the people of South Los Angeles."
"We need to attract sit-down restaurants, full service grocery stores and healthy good alternatives and we need to do in an aggressive manner," Perry said in a statement.
The councilor has said she has pushed for the legislation because of statistics that show her constituents had higher incidence of diseases that doctors link to obesity than other parts of Los Angeles.
"The side effect of a constant diet of fast food is that society pays in the long run in medical costs," she said.
In all of Los Angeles, South Los Angeles has the highest concentration of fast-food chains or restaurants with minimal seating, accounting for 45 percent of all eateries in that area, reports have said.
The Los Angeles law comes after California became the first US state to ban artificial trans fats last week. Under the new legislation, trans fats will be outlawed in restaurants across the state from 2010.