She was arrested at an airport near Moscow in February when cannabis oil vapes were found in her bags.
The double-Olympic winner was convicted of smuggling and possessing cannabis oil in August and sentenced to nine years in a penal colony.
While the use of cannabis is illegal in Russia, Moscow has been accused of using Griner, 32, "as a political pawn".
Defence lawyers sai Griner was on her way to a penal colony, but not where she is being sent to.
The US embassy is normally informed of where international prisoners are held. Griner's team believe they may not be told for two weeks.
Penal colonies are the descendants of Soviet-era enforced labour camps, otherwise known as gulags where prisoners are housed in barracks and perform labour.
At the time of her trial, Griner pleaded guilty, but said she had made an "honest mistake".
Griner - who is seen by many as the greatest female basketball player of all time – unsuccessfully appealed against her.
She apologised in the appeal hearing via video link, saying her imprisonment had been "very, very stressful" and "traumatic".
In Russia, possession of less than 6g of cannabis is normally punishable by a fine or 15 days in detention. Griner is thought to have had less than 1g when she entered Russia to play basketball during the US off-season.
US President Joe Biden had ordered his administration to swiftly "prevail on her Russian captors to improve her treatment and the conditions she may be forced to endure in a penal colony".