The Hull City stopper was ruled out for a month with a shoulder problem earlier this week, with KC Stadium boss Steve Bruce confirming the news at a news conference on Thursday.
And the Scottish Football Association revealed on Friday that Gilks will fill the gap left behind.
Gordon Strachan's men host Georgia in a Euro 2016 qualifier a week on Saturday before visiting Poland three days later.
Gilks, whose only Burnley appearance since signing from Blackpool came in a 1-0 League Cup defeat to Sheffield Wednesday in August, joins Celtic's Craig Gordon and David Marshall of Cardiff City in Scotland's goalkeeping ranks.
The 32-year-old has represented Scotland on three previous occasions.
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