Free and reduced-price school meals are provided by the US Department of Agriculture through the Education Department and are considered an essential service. The USDA has reduced staff somewhat during the partial shutdown, but that should not affect school meal programs.
The School Lunch, School Breakfast, Child and Adult Care Feeding, and Special Milk programs are set to run through February, but there is as of now no indication of how a longer shutdown might affect those programs.
For these programs, meal providers are paid on a reimbursement basis 30 days after the end of a given service month. Carryover funding for many government agencies will be available during an extended lapse to support meal service through the 2019 fiscal year, which ends in September, according to news reports.