She declared a local emergency and that the curfew will run from 8pm Tuesday (1pm Wednesday AEST) until 6am Wednesday.
"We reached a tipping point" after 23 businesses were looted, Bass told reporters.
"Law enforcement will arrest individuals who break the curfew, and you will be prosecuted," she added.
The curfew will be in place in a 2.5sq/km section of downtown that includes the area where protests have occurred since Friday.
The curfew doesn't apply to residents who live in the designated area, people who are homeless, media or public safety and emergency officials.
Los Angeles Police Chief Jim McDonnell said "unlawful and dangerous behaviour" had been escalating since Saturday.
"The curfew is a necessary measure to protect lives and safeguard property following several consecutive days of growing unrest throughout the city," he said.
Earlier on Tuesday, National Guard troops began protecting immigration agents as they made arrests in Los Angeles, an expansion of their duties that had been limited to protecting federal property.
ICE said in a statement that the troops were providing security at federal facilities and protecting federal officers "who are out on daily enforcement operations".
The change moves troops closer to engaging in law enforcement actions like deportations as President Donald Trump has promised as part of his administration's immigration crackdown.
California Governor Gavin Newsom has asked a federal court to block the Trump administration from using the National Guard and Marines to assist with immigration raids, saying it will only heighten tensions and promote civil unrest.
Newsom filed the emergency request after Trump ordered the deployment to LA of roughly 4000 National Guard troops and 700 Marines following protests of the president's stepped-up enforcement of immigration laws.
A judge set a hearing for Thursday.
Newsom said Trump is "pulling a military dragnet" across Los Angeles, during a brief public address on Tuesday.
Trump's immigration crackdown had gone well beyond arresting criminals and was detaining "dishwashers, gardeners, day labourers and seamstresses", he said.
The Marines and another 2000 National Guard troops were sent to LA on Monday, adding to a military presence the police chief says makes it harder to handle the protests safely.
Marine Corps General Eric Smith said on Tuesday that the Marines had not yet been called to respond to the protests and were there only to protect federal officials and property.
Trump on Tuesday described the unrest as an invasion by a "foreign enemy" during a speech at Fort Bragg military base in North Carolina.
He said demonstrators were "rioters bearing foreign flags with the aim of continuing a foreign invasion of our country".
"What you're witnessing in California is a full-blown assault on peace, on public order, and on national sovereignty," Trump said.
"We will not allow an American city to be invaded and conquered by a foreign enemy."
The protests began on Friday after federal immigration raids arrested dozens of workers in Los Angeles.
Protesters blocked a major freeway and set cars on fire over the weekend, and police responded with tear gas, rubber bullets and flash-bang grenades.
The demonstrations have been mostly concentrated downtown in the city of four million and have been far less raucous since the weekend.
Thousands of people have peacefully rallied outside City Hall and hundreds more protested outside a federal complex that includes a detention centre where some immigrants are being held following workplace raids.
The Los Angeles Police Department said there have been more than 100 arrests. The vast majority were for failing to disperse, while a few others were for assault with a deadly weapon, looting, vandalism and attempted murder for tossing a Molotov cocktail. Seven police officers were reportedly injured, and at least two were taken to a hospital and released.
On Tuesday, a few dozen protesters gathered peacefully in front of the federal complex, which was quickly declared an unlawful assembly.
Police issued a dispersal order and corralled the protesters, telling members of the media to stay out to avoid getting hurt.
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