The district recently changed its public reporting system to show a cumulative case count among students and staff for the school year.
City Health department, EMS have already begun small-scale city-run distribution.
Two campuses account for more than half of the 221 people quarantining.
The most severe restrictions will begin Friday, Feb. 12.
A special district per-pupil allotment dropped from $100 to $60 per student.
The news comes after a surge of cases at the university.
A resolution, likely to go before the full City Council next week, would also restrict new late fees for Entergy customers.
Attendance rates are down and chronic absenteeism is on the rise as the pandemic carries on.
Students returned to school Monday after a three-week campus closure.
The effort will help identify newer variants of the disease.