The 38-year-old actor, Michael Fassbender, and the 26-year-old actress had been dating for nine months since meeting on the set of 'The Light Between Oceans', in which they play a lighthouse keeper and his wife who raise a baby they rescue from an adrift rowboat.
Us Weekly reports that the pair - who were last photographed together in May at the Monaco Grand Prix - have now called time on their relationship.
'The Danish Girl' actress Alicia is not the first co-star Michael has dated, he had a relationship with 'X-Men: First Class' star Zoe Kravitz from 2010 to 2011 and from 2012 to 2013 he romanced 'Shame' actress Nicole Beharie.
However, he has previously insisted that his career has hindered his love life.
Michael said: "I'm kind of selfish with the hours that I put into the work. I think the longest relationship that I've been in was two years... I started doing this when I was 17, so I guess in my dating, adult life, that kind of covers it."