Based on David Ebershoff's novel of the same name, the movie narrates the life of Lili Elbe (Eddie Redmayne), one of the first known recipients of sex reassignment surgery.
As Wegener, Vikander gave a compassionate performance as Gerda, who struggles to come to terms with her husband's decision to become a woman but eventually ends up being his biggest moral support.
Vikander, 27, was a surprise early winner in the category which many thought belonged to Kate Winslet as she had won the Golden Globe and Bafta awards.
The young star looked emotional as she took to stage to accept her award from last year's best supporting actor winner J K Simmons.
"Thank you Academy for this recognition. I share my award with my incredible crew from the film. Thank you my director Tom (Hooper), thank you Eddie for being the best acting partner. In the end, I would like to thank my mom and dad who believed in me," the actress said as she rushed through her speech.
The Sweden native's other roles include "A Royal Affair", "Testament of Youth" and "Ex Machina".
The early Oscar win is sure to give her rising career a major boost.
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