Leonne Zeegers, 57, received a passport with the gender designation X, instead of M for man or V for woman.
Born male, in 2001 Zeegers had surgery to become female, but now identifies as intersex.
Zeegers won a lawsuit, with judges ruling that preventing a registration as gender neutral amounted to a "violation of private life, self-determination and personal autonomy".
About 4% of the Dutch public identifies as neither male nor female, the BBC's Anna Holligan reports from The Hague.
Despite the ruling, it remains a matter for courts to decide if an individual should receive an X designation for gender.
Several countries already offer a gender-neutral option in passport applications. They are: Argentina, Australia, Canada, Denmark, India, Malta, Nepal, New Zealand and Pakistan.
Our correspondent says the Zeegers case has galvanised LGBT support groups to ask the Dutch government to change existing legislation, to allow anyone to identify as a third gender.
Currently, all UK passport holders have to specify whether they are male or female.
In June a campaigner lost a High Court challenge to the UK passport rules - their bid for an "X" category was rejected.
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