Clinton had called for her release, after re-tweeting a BBC article about the player’s predicament.
But the Moscow court announced on Thursday it was keeping her in custody.
“The court granted the request of the investigation and extended the period of detention of the US citizen Griner until May 19,” the court said, according to Tass.
Arguably the greatest female basketball player of all time, the double Olympic gold medallist has been called the “Tom Brady of her sport”.
Ms Griner went to Russia to play during the US league’s off-season.
In one of the last public sightings of her, captured on CCTV, the player is seen walking through security at a Moscow airport trailing a small, black suitcase.
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