The Zamalek striker, who finished his loan spell with English side Wigan Athletic, was bizarrely injured during Egypt's 1-0 away victory over Oman on Saturday.
He jumped for joy to celebrate Mohamed Abou-Treika's second-half goal to inadvertently bash heads with teammate Ahmed Eid.
Zaki was substituted afterwards, prompting fears over his availability for the crunch World Cup qualifier against Algeria on June seventh.
"Zaki is ok. His injury is negligible," Gharib told Dream TV after the match.
Gharib was satisfied with the players' display against Oman in the only warm-up for the anticipated clash at Algeria.
"The players exerted lots of efforts today, the high temperature did not affect their performances," he said.
"I'm confident because that win lifted the players' morale ahead of our next game against Algeria."