"We fined Zidan because he did not even answer our calls nor explain his action," Zaher told FilGoal.com.
Zaher declined to disclose the amount of money Zidan will be deducted.
The Borussia Dortmund man failed to show up for Egypt's 3-3 draw with Guinea in Cairo on Wednesday.
His German club wrote to the FA to inform them that he was injured.
However, the FA were still infuriated that Zidan, who played in Dortmund's 4-1 Bundesliga defeat to Hamburg on Saturday despite his apparent injury, did not clarify the matter himself.
It remains to be seen whether Egypt coach Hassan Shehata would include him in his plans for the upcoming World Cup qualifier at Rwanda next month.
Reports suggested that Shehata would snub hum for the anticipated encounter.
"Our decision to fine Zidan has nothing to do with the technical staff's stance. Shehata is free to decide whether to recall him," Zaher added.
The six-time African champions lie second in Group C of the qualifiers with four points from three games, three behind leaders Algeria.
Only the group winners will reach next year's South Africa finals.