She was honoured for her role in the acclaimed Nordic drama 'The Danish Girl', playing Danish artist Gerda Wegener in a love story about how she and her fellow artist husband Lili Elbe played by British actor Eddie Redmayne, navigate his journey as a transgender pioneer.
"Eddie, there you are. Thank you for being the best acting partner. I could have never done it without you. You raised my game," Vikander said late on Sunday in Hollywood in her acceptance speech, before sharing a congratulatory kiss with her actor boyfriend Michael Fassbender.
"I want to thank my friends and my mum and dad – thank you for giving me the belief that anything can happen, even though I would have never believed this."
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The last Swedish actor to win an Academy Award was Ingrid Bergman in 1974 for her role in The Orient Express.
Vikander bested fellow nominees Jennifer Jason Leigh ('The Hateful Eight'), Rooney Mara ('Carol'), Rachel McAdams ('Spotlight') and Kate Winslet ('Steve Jobs').
Her co-star Redmayne however, who had been nominated for best actor for the same movie, lost out to to Leonardio DiCaprio and 'The Revenant'.
'The Danish Girl' had also been nominated in the categories for best costume design and production design, but was beaten to the win by 'Mad Max: Fury Road'.
The action flick also took home the best makeup and hairstyling category, beating Swedish movie 'The 100-Year-Old Man Who Climbed Out of the Window and Disappeared' about a man who escapes from his retirement home.