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 will now miss Scotland's third qualifier in Warsaw after the Scottish Football Association's confirmed Hanley's absence on Twitter.
His inury means Brighton's Gordon Greer, Ipswich's Christophe Berra and Aberdeen's Mark Reynolds will fight it out as possible replacements as they look to halt Poland's unbeaten run in the qualifying rounds.
Victories against Gibraltar and Germany have put them top of Group D - ahead of the Republic of Ireland on goal difference - and Martin highlighted 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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