"He hasn't trained because he's not in condition to do so," manager Jose Mourinho told a news conference on Monday.
"It's the same problem that he is having, it's simple. Let's see what happens for the next weekend."
Costa, who has made a stunning start to his Chelsea career with nine Premier League goals since joining from Atletico Madrid, has been struggling with a hamstring injury and did not play in the 2-1 defeat of Crystal Palace on Saturday.
Chelsea are well-placed in Group G with four points from their opening two fixtures but have several players unavailable for the visit of the Slovenian outsiders to Stamford Bridge.
Midfielders John Obi Mikel, Andre Schurrle and Ramires will all play no part while striker Didier Drogba is not fit enough to play for 90 minutes, according to Mourinho.
"Mikel made a big effort to be available for the weekend. He came back from the national team with a foot problem. He can't play tomorrow," he said.
"Didier is not in condition to play 90 minutes but he can play."
He confirmed that 17-year-old reserve team striker Dominic Solanke would start on the bench.
While Chelsea are expected to bag a comfortable three points, Mourinho warned that Maribor should not be taken lightly and that he would not be resting any players ahead of next weekend's Premier League clash with Manchester United.
"The group is not an easy one," Mourinho said.
"(Maribor) are a difficult team and I am happy because I think my players have the feeling they are a difficult opponent so we must play with the best we have. We are not going to give any favours by resting people or changing the team.
"We have four points in our group which is not bad but we need seven out of these three matches as that gives us a little bit of stability for the second part," he added.
(Reporting by Martyn Herman, editing by Alan Baldwin and Pritha Sarkar)
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