The singing superstar and her rap star partner were together in a trailer on the property at the time of the Sunday afternoon shooting, while other family members and staffers were in the Beverly Hills-area home, Los Angeles County District Attorney Nathan Hochman said outside a court hearing.
Ivanna Lisette Ortiz, of Orlando, Florida, faced the LA court on Tuesday, local time.
Deputy Public Defender Jamarcus Bradford at first entered a plea of not guilty on her behalf, but then withdrew it in favour of postponing arraignment until March 25.
She was ordered held on $US1.8 million ($A2.5 million) bail. Ortiz wore blue jail clothes with her blonde hair in braids and spoke to the lawyer through a glass divider.
The LA County Public Defender's Office said in a statement it could not comment on the pending case against Ortiz.
"As in every case, we will work to ensure that our client receives the full protections guaranteed under the Constitution," the statement said.
Ortiz could get life in prison if convicted on all charges. The three counts of firing at a dwelling were for Rihanna's house, her trailer, and a neighbour's house, prosecutors said. The 10 assault counts were for Rihanna and family, two staffers and two people in the neighbouring house.
"LA-based celebrities should not be additionally worried because of this," Hochman said, "in large part because of the response of the police."
He praised officers for arresting Ortiz soon after the shooting, several kilometres to the north in the suburb of Sherman Oaks.
Judge Theresa McGonigle issued a protective order for Ortiz to stay away from Robin Fenty and Rakim Mayers - the legal names of Rihanna and A$AP Rocky - and their home.
McGonigle also said Ortiz is not allowed to possess any firearms or ammunition along with several other conditions.
The hearing was held in a courtroom a few floors from where Rocky went through a trial where he was acquitted just over a year ago. Rihanna was often in attendance, sometimes with their sons.
And the lead prosecutor in the new case is Alexander Bott, the deputy district attorney who successfully prosecuted rapper Tory Lanez in a trial where he was convicted of shooting hip-hop star Megan Thee Stallion in the feet.
Hochman would not say where any of the bullets landed, would not say how long Ortiz had been in California, or discuss her motivation or any connection to Rihanna, saying all were under investigation.
Public records show her most recent address was in Orlando and that she has been a licensed speech pathologist for more than a decade.
Voicemails and other messages left by The Associated Press, including an email sent to the public defender's office, were not immediately answered.
AP also sent emails seeking comment from Rihanna's publicist and manager.
KABC-TV broadcast video that appeared to show five bullet holes in the home's front gate. The news station obtained police dispatch audio that says 10 shots were fired.
In 2018, a man was accused of breaking into another home belonging to Rihanna in the Hollywood Hills and spending 12 hours there.
The man pleaded no contest to felony counts of stalking and vandalism and a misdemeanour count of resisting arrest in 2019. He was sentenced to probation.
A nine-time Grammy Award winner, Rihanna has 14 No.1 hits on the Billboard Hot 100, including We Found Love, Work, Umbrella and Disturbia. She founded the makeup brand Fenty Beauty in 2017.
She and A$AP Rocky announced the birth of their third child, a girl named Rocki Irish Mayers, in September.
