The Belgian international has been in scintillating form so far this season, netting eight goals in all competitions, but he will sit out the visit of the Belarusian champions due to an ongoing back injury.
Hazard is also now doubtful for Chelsea's Premier League clash with Burnley on Sunday, so boss Maurizio Sarri appears happy to wrap the 27-year-old up in cotton wool given the west Londoners are two wins from two in the Europa League this season.
Midfielder Jorginho will also sit out Thursday's match, with Sarri confirming he plans to rest the Italy international, while youngster Ethan Ampadu remains sidelined with a knee injury.
Sarri is expected to give players in need of game time a chance to impress, with Andreas Christensen and Ruben Loftus-Cheek pushing for starting roles.
Despite taking the opportunity to rotate his side, Sarri is still wary of the threat his side will face when they take on BATE, who currently sit nine points clear at the top of the Belarusian Premier League.
"These two matches in Europe have been difficult. They've not been easy," Sarri said.
"We have to prepare our minds to play another difficult match because this opponent during the season has lost only four times I think. I think it will be very difficult as this season they've done better away from home."