The Raiders placed Hurst on the reserve/COVID-19 list Tuesday, but it was unclear whether he had tested positive for the virus.
The Raiders' facility will be open Wednesday, according to Russini.
Being placed on the reserve/COVID-19 list does not necessarily mean a player has tested positive for the coronavirus; it can also mean the player has come in close contact with someone who has the virus.
NFL teams are not allowed to disclose why a player was placed on the list.
Hurst wasn't one of the 10 Raiders players fined a total of $165,000 by the NFL on Monday for violating coronavirus protocols at a charity event hosted by tight end Darren Waller, a source told ESPN's Dan Graziano on Tuesday, confirming an NFL Network report.