Although he was included in Zamalek squad for the CAF Champions League encounter, Zaki failed to link up with his teammates for their trip to Abidjan.
The Egypt striker said he missed the match due to injury but Zamalek doctor Abdullah George refuted his claims.
Zamalek progressed to the competition's round of 16 on penalty shootout after a 2-2 aggregate draw with the Ivorian outfit.
The Cairo giants' board has questioned Zaki over his attitude on Friday.
"I stood by the player because he is one of Zamalek's top stars," Helmi told FilGoal.com.
"However, he must be punished. I believe a fine will be an adequate penalty for his action."
Match Postponed
Helmi is pleased that the Egyptian FA competitions' committee has agreed to postpone Zamalek's league game against Suez Cement for one day.
The match will be played on Monday instead of Sunday upon Zamalek request.
"The players needed some rest because we had a hectic schedule recently. Players' exhaustion contributed to our defeat against Masri," Helmi said.
Zamalek, who aim to finish second in the league in order to play in the Champions League next season, were handed a 2-1 home defeat to Masri on Thursday.