Damon, along with wife Luciana Barroso, and three other children - Isabella, 13, Gia, 12, and Stella, 9 - stayed in Ireland.
"She's (Alexia) in New York City and she had Covid-19 really early on along with her roommates and got through it fine," Damon told a radio station in an interview, reports usatoday.com.
"We'll reunite with her at the end of the month. But everybody's OK, obviously Lucy's mom and my mom - it's scary for that generation."
The Damon family is well-equipped for quarantine in a foreign country.
"We've got what nobody else has, which is actual, live human beings teaching our kids," he said.
"We feel guilty. We've got this kind of incredible setup in this place that's absolutely gorgeous."