In response to an article about the engagement, Hendrix, 48, jokingly tweeted: "Watch out for those twins."
In the 1998 film, Hendrix stars as Meredith Blake, who gets engaged to Nick Parker (Quaid). Parker is dad to twins -- Hallie and Annie (played by Lindsay Lohan) -- whom he shares with ex-wife, Elizabeth James (played by the late Natasha Richardson).
The movie follows the twins, who were separated at birth, as they create a grand plan for a way to get their dad and mom back together.
Of his real-life engagement, Quaid gushed to Extra about the "spontaneous" moment.
“It has been kind of a month-and-a-half plan — I wanted it to be private," he noted.
The Sharks singer revealed he waited for the perfect sunset while the pair were visiting Turtle Bay in Oahu to pop the question.
“She was actually taking a selfie of us, and I put the ring in front and said, ‘Will you marry me?’ And then she fell down," said Quaid.
Fox News' Stephanie Nolasco contributed to this report