The court ordered that 29-year-old Burkov be kept in custody without specifying how long.
"You will be remaining in custody", the judge ruled, citing the gravity of charges and absence of family ties in the United States.
The judge added that the ruling may be reviewed at a later date if circumstances change.
On Tuesday, US prosecutors said Russian national Alexei Burkov would face a sentence of up to 30 years in prison if found guilty in the United States.
On Monday, he was extradited from Israel to the United States.
The Russian government has filed charges against him and demanded he be extradited to the country of origin and not the United States.
Burkov was detained in Israel at the request of the US administration and accused of running two websites for hackers, including one that was selling stolen bank card numbers that were used in more than $20 million worth of fraudulent purchases.
Prior to his extradition to the United States, Burkov spent almost four years in Israeli custody fighting unsuccessfully to be sent home while the local authorities enforced a ban on his case in the media.