Chelsea head coach Maurizio Sarri will continue to restrict the 27-year-old's game time in Belarus, though he insists it is not a gamble to include him in the squad.
"From our doctor there is no risk, otherwise he would stay at Cobham [training ground]," Sarri told Chelsea’s official website.
"In the last match he played 30 minutes, the best for [the BATE game] is that he plays 45 to 50 minutes."
Fabregas was excluded from the travelling party due to illness, while Morata – who has scored four goals in his past four Premier League appearances – has been granted a rest.
"[Morata] played for three matches in a row, so I thought it was better to rest at Cobham and have good training. The only problem is Cesc. He had a fever," the Chelsea boss added.
Many expected Morata to feature again on Thursday after his recent good form, with Sarri suggesting that the striker needed to work on his mental fragility following his side’s win over Crystal Palace.
Asked if it would be better to play the Spain striker to help maintain his resurgent form, the Italian added: "No. I think it is the opposite.
"Morata stayed in Cobham just to rest and then just to have training. I think it is better for him to stay fit with two or three trainings than only with matches.
"It is normal. Sometimes it is better to rest than always play. If they only play they will lose that physical quality."
Marcos Alonso, David Luiz, Antonio Rudiger and Victor Moses also did not make the trip, but Olivier Giroud could feature after missing the Palace match with a muscular issue.