The singer, 38, was at home at her Beverly Hills mansion when it was struck by 10 shots on Sunday, with Ivanna Ortiz, 35, charged with attempted murder, on suspicion of firing an assault rifle at the property.
Page Six reports a source told the outlet "the singer is taking extra security precautions and has even rescheduled an upcoming photo shoot because of the shooting".
Another insider said Rihanna "doesn't understand" why her family was targeted.
They added the Disturbia performer has been left "freaking the f**k out" after the attack using an AR-15 semi-automatic rifle.
"Rihanna heard the shots, but was initially confused about what happened," a source said.
"Even with a great security team in place, it's scary to realise that something like this can still happen."
"(It was) terrifying (but Rihanna is thankful) everyone is safe."
Rihanna shares the property with her longtime rapper partner A$AP Rocky, 37, and their children RZA, three, Riot, two, and six-month-old Rocki.
It has also been reported the alleged shooter reportedly targeted the singer's mansion days after posting a threatening message directed at the performer on social media.
According to the Daily Mail, the suspect posted an abuse-filled message directed at Rihanna on Facebook on February 23.
Sharing an image of herself wearing a leopard-print top, she is said to have written: "@badgalriri Are you there? Cause I was waiting for your AIDS 5-head self to say something to me directly instead of sneaking around like you talking to me where I'm not at."
In other social media posts, the Mail said Ortiz declared she was "threw [sic] with Rihanna" and described the singer as a "turn hiding bitch".
Officers allege Ortiz fired the shots from a white Tesla before fleeing the scene.
The LAPD's Robbery Homicide Division is investigating the incident, police confirmed, with Ortiz now facing an attempted murder charge.
Radio dispatch recordings of the incident, heard by the Los Angeles Times, said at least 10 shots were fired from the vehicle before the driver fled.
A police helicopter later located a Tesla in a parking lot in Sherman Oaks, where Ortiz was arrested.
According to the Mail, Ortiz has previous arrests in Florida for domestic violence, careless driving and violating pre-trial release conditions.
In December, she is said to have filed an appeal seeking to overturn a decision in her home state that granted custody of her child to her former partner.
Ortiz has also promoted a "Praying Woman's Journal" on YouTube, where she reads from the Bible daily.
She has also posted images of herself posing with pageant trophies and has said she won Miss Teen Illinois Latina Princess in 2006.
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