When they bring her back to the mainland during his shore leave, they find out that a local woman, played by Rachel Weisz, has been looking for her missing husband and baby daughter. In October, Fassbender and other members of the cast and crew celebrated Vikander's 26th birthday at a hotel in the Marlborough region, local outlet nz reported.
Also that month, the actor and actress were photographed together at a local spa and massage parlor, as seen on the shop's Facebook page.
In 2013, his role as slave owner Edwin Epps in the slavery epic 12 Years a Slave was similarly praised, earning him his first Oscar nomination for Best Supporting Actor.
In 2013, Fassbender appeared in another Ridley Scott film, The Counselor.
In 1975 Douglas produced One Flew Over the Cuckoo's Nest, having acquired the rights to the Ken Kesey novel from his father.
The film received critical and popular acclaim, and won the Academy Award for Best Picture, earning Douglas his first Oscar as one of the film's producers.
In 2015, he portrayed the title role in the Danny Boyle-directed biopic Steve Jobs (2015), and played Macbeth in Justin Kurzel's adaptation of William Shakespeare's play.
"I'm kind of selfish with the hours that I put into the work," he told the mag.
Fassbender plays Tom Sherbourne, a lighthouse keeper who lives on an island in Australia with his wife Isabel, played by Vikander.
On board are a dead man and a living baby, who they raise as their own and name Lucy.
PHOTOS: Celeb splits of 2015 Fassbender, 38, and Vikander, 26, first met on the set of their film, , and continued spending time together in late 2014, fueling dating speculation.
They were last photographed together in May at the Formula One Grand Prix in Monaco, where they looked affectionate and happy as they enjoyed the races.