Dudley councillor Anne Millward said the unidentified school, which she says is over the Sandwell border, is "virtually the most deprived one in western Europe".
But she claims not one parent of the Year 6 group, which had been sent home due to coronavirus, came to collect meals on their child's behalf.
She made the revelation during a debate on free school meals at a Dudley Council health meeting.
Councillor Millward told the Health and Adult Social Care scrutiny committee: "There's a school that last week had to shut down one year group.
"It is in a very deprived area and over 50 per cent of the children qualify for free school meals.
"The school staff were scratting about and ringing around the parents to say 'we have got your meals here'.
"Not one parent wanted to come in for the meals. Not one. And it just shows that yes, it is an issue that we all care about.
"But these parents were not prepared to come to school and fetch the school meals, the pre-packed grab bag for the child, saying 'no, leave it, we are alright'.
"It is not everybody who is taking this up even though they are entitled to it.
"It is not because of pride. It is because they can't be bothered to come to the school to fetch them."
Asked about the incident after the meeting, Tory councillor Millward told the Express & Star: "The school isn't in Dudley but comes under Sandwell.
"It is absolutely disgusting. This school is in one of the most deprived areas of western Europe. It is virtually the most deprived school in western Europe.
"It makes me wonder who is complaining about free school means. Is it the parents themselves? I am not being political here."