Cavani returned to Uruguay earlier in the week for personal reasons and will not be back in time for Saturday's match.
The 27-year-old has scored 14 goals in 22 league appearances since moving from Napoli at the start of the season but the Ligue 1 leaders will have to do without him against mid-table Bastia.
It is unclear whether he will return in time for their UEFA Champions League last 16 second leg tie with Bayer Leverkusen on Wednesday.
"Cavani will not play tomorrow for the match against Bastia," Blanc said.
"I think apart from Cavani no other player will be unavailable.
"Christophe Jallet is back in the group, this will allow us to be able to breathe a little about (Gregory) Van der Wiel."
Blanc is wary of the threat that Bastia will pose as PSG seek to extend their eight-point lead over Monaco, who host Sochaux later on Saturday.
"We know that we are in a very favourable position. But we must stay focused," the coach added.
"Bastia will want to exploit tomorrow, they are very motivated.
"We will try to be very effective in recovering the ball."
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