Newsom wrote to Trump to request a U.S. Navy Mercy Ship - a floating hospital - to dock at the Port of Los Angeles.
"Our state and health care delivery system are significantly impacted by the rapid rise of COVID-19 cases", the letter said.
The new stay-at-home order is meant to reduce that figure, Newsom said Thursday.
As of Thursday evening, California had about 908 cases of the coronavirus and 18 deaths, a tally that's lower than states including NY and Washington but sure to increase as testing accelerates.
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 in the day Newsom projected that roughly 56% of the state's population will be infected with the virus in the next 8 weeks.
California is one of the main centres for the coronavirus in the U.S., although with fewer cases than NY at the moment.
Kevin McCarthy, a Republican congressman from California, wrote on Twitter: "I hope Governor Newsom consulted with a lot of experts before he chose to shut down 12 percent of the nation's population".
Detroit automakers idle USA plants to combat coronavirus outbreak
Early today, TechCrunch published an internal Tesla memo detailing employee instructions for its Fremont-based factory. We have time to review best practices when the plants reopen, and we prevent the possible spread of this pandemic.
This story has been corrected to show that Newsom said up to 20% of people infected by coronavirus, not 20,000 people, could be hospitalized. Coming on top of a $1 trillion economic bailout that will include cash payments for individuals and families, it is small relief to a besieged populace that has seen the economy crater and millions of jobs vanish in the face of the Covid-19 assault.
"This is a moment we need to make tough decisions", Mr Newsom said.
However, he did offer a glimmer by saying he didn't expect it would last "many, many months".
"If we're to be criticized at this moment, let us be criticized for taking this moment seriously", he said. He said that money would be needed to do things like set up state-run and mobile hospitals, housing options to help people socially distance and testing and treatment for people without health insurance.
Residents across the entire state are being asked to stay at home, except for essential purposes.
Those expectations "assume we're just along for the ride", Newsom said.
"I order that Californians working in these 16 critical infrastructure sectors may continue their work because of the importance of these sectors to Californians' health and well-being", Newsom wrote in his order.
The order took effect at midnight Friday, but what exactly does it entail?