The Blackburn Rovers defender had formed a solid partnership with Russell Martin at the heart of Gordon Strachan's defence - helping Scotland to a 1-0 win over Georgia on Saturday.
However, the 22-year-old appeared to pick up a knee problem at Ibrox and as such will miss Scotland's third qualifier in Warsaw this week.
A tweet from the Scottish Football Association's official account confirmed Hanley's absence.
Poland have taken maximum points from their fixtures against Gibraltar and Germany, and Martin has highlighted Bayern Munich striker Robert Lewandowski as their primary dangerman.
"We will watch all the videos on him before Tuesday," said Martin.
"He is a fantastic player but the staff here prepare us for everything.
"I'm sure we have seen enough of him in the Bundesliga with the goals he has scored to know how dangerous he is. So we will be ready."
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