Hummels sustained a thigh injury in the 6-1 league win against Stuttgart but it was not discovered until a day later, Klopp told reporters.
"Mats had problems with his thigh after the game but it was only the morning after that he noticed them," he said.
"He is 97.5 percent unlikely to play," said the German, who last week signed a contract extension until 2018. "We did try everything."
Greece international Sokratis Papastathopoulos, who scored a goal against Stuttgart last week, will most likely replace Hummels in the central defence for Wednesday's match.
Dortmund are level on six points with the north London club and Napoli at the group stage halfway mark. Olympique Marseille have yet to score a point.
Klopp said he expected his team to have the same commitment they had shown so far, including in a 2-1 win in London last month.
"We expect an intense game with a lot of one-on-ones. At this level there are only few surprises with regard to our opponents' overall strength," said Klopp. "If Arsenal are stronger tomorrow than they were at home it will be because we let it happen."
Klopp will return to the Dortmund bench after spending the last two European matches in the stands following a suspension stemming from their opening defeat to Napoli.
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