He will be replaced by young understudy Ryan Bertrand while the Londoners are again without vice-captain Frank Lampard (calf injury).
Chelsea also have fitness doubts over defender David Luiz (ankle) and midfielder Juan Mata (hamstring) who both missed Saturday's 1-1 draw at Swansea City.
"Ashley Cole won't be available. He has a problem with his hamstring but shouldn't be out too long," coach Roberto Di Matteo told reporters on Tuesday.
"Ryan Bertrand has always performed well for us when he's played and I have full confidence he will play a great game."
Second-placed Chelsea, who have skipper John Terry available to return to the heart of the defence after suspension, need to avenge last month's 2-1 defeat in Donetsk in order to join Shakhtar at the top of the group table on seven points.
"I think we will need to be at our best. We need a perfect game," said Di Matteo. "Every player on the pitch needs to perform at the highest of their ability.
"In Donetsk their early goal helped them massively. It's important we start well and get the crowd behind us and draw confidence from a good start."
The Italian said his team usually responded well to high-pressure games like the one they face at Stamford Bridge.
"This team has a strong mentality and we have the experience of performing in big games like this, not to feel the pressure too much," Di Matteo explained.
"We've had must-win games before and tomorrow is another one like that. We are strong at home... and we will be fired up to win."
