The Miral director popped the question to the Danish model following an eight-month romance, according to Page Six.
This will be the third marriage for Schnabel, who most recently split from Miral screenwriter Rula Jebreal in June 2011 after four years together.
His two previous marriages were with designer Jacqueline Beaurang and actress Olatz López Garmendia, both of whom he has children with.
Schnabel has directed several critically-acclaimed films including Basquiat and The Diving Bell and the Butterfly.
Watch a trailer for Miral below: