At a Monday afternoon press conference, county public health director Dr. Barbara Ferrer said people should try not leave their homes for groceries or medications, but should instead arrange for them to be delivered, if necessary.
"If you have enough supplies in your home, this would be the week to skip shopping altogether," she said.
The recommendation comes as the number of cases across L.A. County topped 6,000. The county's death toll now stands at 147.
Those venturing out to the stores will soon see some major changes to keep customers and employees safe.
Many stores are already enforcing physical distancing and limiting the number of people allowed in at a time.
Ralphs is limiting the amount of shoppers allowed inside to 50% capacity to allow for improved physical distancing.
One-way aisles are also being implemented by many chains, like Vons.
Walmart was the first to announce the new measure aimed at helping customers keep their distance. Vons says it is also joining the effort.
Shoppers are taking the opportunity to take one last trip to the store before hunkering down at home.
"We went back and forth, me and my sister, about whether to come out or not. We're gonna stay in for two weeks, so we decided to make one last (trip.) We're almost out of water," Studio City resident Kina Cosper said. "We're here and then we're like done for two weeks."
Ralphs, which is owned by Kroger, has installed plexiglass at checkout lines. The chain is also encouraging employees to wear face masks and gloves.
Globally, the number of people dying appeared to be slowing in New York City, Spain and Italy. The news was cautiously welcomed by leaders, who also noted that any gains could easily be reversed if people did not continue to adhere to strict lockdowns.
The U.S. is still awaiting the peak, and Surgeon General Jerome Adams offered a stark warning about the expected wave of virus deaths.
"This is going to be our Pearl Harbor moment, our 9/11 moment,'' he told "Fox News Sunday."
The Associated Press contributed to this report.