According to the Ohio Department of Commerce, if a minor has all necessary paperwork completed and is unable to get the permit processed due to school closure, the completed paperwork may itself stand in the place of the physically printed permit. Employers should keep the paperwork on file, just like they would the permit. The formal permit should be processed as soon as the school is reopened.
As a reminder, hour restrictions outlined in Ohio Revised Code Section 4109 are still in place for any week that was not a pre-planned school holiday (i.e., spring break) and the prohibited/hazardous occupation restrictions are still active.