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The former Aberdeen and Nottingham Forest stopper played three out of the four games in the group before he was sent off during Scotland's win in North Macedonia.
He was suspended for the final match in the group - a defeat to Slovenia at Hampden - but will be available for a return in the final games next month against North Macedonia at home and Switzerland away.
However, he was ruled out of Dinamo Zagreb's midweek home win against Rijeka because of injury and faces a race against time to play for his country next month.
Dinamo Zagreb assistant manager Sandro Bloudek said: "Everyone in the squad is fit apart from Scott McKenna.
"He suffered a muscle injury in his back and was not available for the game."
McKenna has won 54 caps for Scotland and was part of the World Cup squad, where he played the final match against Brazil in Miami.