Mayor Eric Garcetti said the orders would require the shuttering of all indoor shopping malls, playgrounds and other gathering places at least until the end of the month.
"We're taking this urgent action to limit the spread of COVID-19 and save lives," Garcetti said at an afternoon news conference.
The orders are similar to so-called "shelter in place" directives given in more than a dozen Northern California counties.
California has been among the hardest hit states in the outbreak of COVID-19, with more than 1,000 confirmed cases and at least 18 deaths.
Earlier on Thursday, California Governor Gavin Newsom asked President Donald Trump to send a U.S. Navy hospital ship to the port of Los Angeles "immediately" as the state braces for an expected surge in the number of coronavirus cases over the next eight weeks.
Newsom said in a letter to Trump that experts were projecting that roughly 56 percent of Californians, or about 25.5 million people, were expected to contract the respiratory illness over the next eight weeks.