The right-back suffered a fractured jaw in Saturday’s 2-0 win over Atlanta United FC in Major League Soccer.
He will be re-evaluated after four or five weeks before a definite date for his return to action can be finalised.
“Harry has a fractured jaw," Porter said, as reported by his club's official website.
"As you know with fractured jaws, they wire your jaw shut, so they’ll have his jaw wired shut for a period of four to five weeks, and then from there, it’ll be a matter of his fitness and nutrition," said head coach Caleb Porter .
“You never like to lose a quality player like him from your team, but that’s why we have a squad and it opens up an opportunity for Hector [Jimenez].
"And we are very confident in Hector and comfortable with him, so we’ll have to manage this four to five weeks and then several weeks after that without Harry.
"I don’t replace players. We don’t replace Harry, but Hector’s been in the wings waiting and ready and we’re confident in his ability to step in and get the job done for us and that’s why we have a squad and I preach that on a daily basis.”
Afull has been instrumental to Crew's good start to the season, having started all five games played thus far.
Ghana will be keenly monitoring the 32-year-old's situation as the Africa Cup of Nations is only two months away.
The Black Stars already have concerns about the injured Leicester City ace Daniel Amartey, who is yet to return to action since picking up an ankle injury in October last year.