Nylander is Unibet's chief executive, which has been accused of breaking France's lottery laws by allowing French citizens to use Unibet's website.
The allegations were made by France's lottery monopoly, Francaise des Jeux, and the horse betting monopoly PMU.
The claim is disputed by Unibet, which was founded ten years ago in Sweden, and operates in the UK and Malta.
Swedish politicians have criticised the arrest, which was made at Amsterdam's Schipol Airport at the request of the French authorities. He was released, but is not allowed to leave Holland until a French court rules on the case.