Fleck is due to join up with the team on Sunday, so will not travel to Albania for the first Nations League clash this month.
He has been selected with a view to being available for the return match at Hampden park, against Israel on Tuesday.
To date, eight players have withdrawn from McLeish's squad, and so the Scotland boss was forced to call up further players to reinforce his side.
Fleck seems like a suitable replacement, having appeared in all but one of club side Sheffield United's matches so far this season.
27 year old is yet to represent his country at senior level, but he has previously done so for the lower age divisions.
Scotland sit second in their group, on three points with a game in hand on Tuesday's rivals Israel, who sit top on six points.