The move comes after Beckinsale has made headlines for her cheeky clapbacks to comments criticizing her relationship with 25-year-old Saturday Night Live comic Pete Davidson, who also stays away from social media.
Davidson and Beckinsale have been spotted together multiple times over the past three months since flirting together at a Golden Globes afterparty in January.
Earlier this month, they were photographed locking lips at a New York Rangers hockey game at Madison Square Garden, instantly sparking funny memes about the reactions from celebrities sitting around them.
Most recently, they went to dinner with Beckinsale's mom, across Judy Loe, and stepfather Roy Battersby, leading fans to speculate that the relationship is getting serious. The day before that, the Underworld actress and Davidson were spotted kissing in the backseat of a car after attending the premiere of the Mötley Crüe biopic, The Dirt.
During a "Weekend Update" sketch of a Saturday Night Live episode this month, Davidson spoke out about critics of the 20-year age gap between him and Beckinsale.
"Weekend Update" host Colin Jost asked if Davidson had any new life developments, "like a new girlfriend." Davidson was reluctant to answer at first, but ultimately opened up about it.
“OK, yeah. Apparently people have a crazy fascination with our age difference,” he said. “But it doesn’t really bother us. But then again, I’m new to this.”
"But then again, I'm new to this. So if you have questions about a relationship with a big age difference, just ask: Leonardo DiCaprio, Jason Statham, Michael Douglas, Richard Gere, Jeff Goldblum, Scott Disick, Dane Cook, Derek Jeter, Bruce Willis, Harrison Ford, Tommy Lee, Alec Baldwin, Sean Penn, and whoever the president of France is," he said in rapid-fire succession. "Mel Gibson, Billy Joel, Mick Jagger, Sylvester Stallone, Eddie Murphy, Kelsey Grammer, Larry King, Larry King, Larry King, Rod Stewart and Donald Trump."
A source close to Beckinsale previously told PEOPLE that she's "very happy with Pete. They have really similar senses of humor and she's always laughing with him."