Lord Prior said it was "strange" that parts of Britain was struggling with nutrition but also with obesity.
He suggested it was a contradiction that poorer areas, who rely more heavily on foodbanks than more affluent ones, also have higher rates of obesity - a symptom of eating too much.
The health minister's comment comes as new figures reveal 1 in 3 primary school leavers are now overweight or obese, and that children in poorer areas are up to twice as likely to be overweight or obese as kids from richer areas.
Most Revd Justin Welby said in response to Lord Prior: "Our experience in the Church of England, involved in the vast majority of food banks across the country, is that between 35% and 45% of people coming to get support from food banks report that the reason they are running out of food is to do with changes to the benefits system and sanctions."
The peer replied: "I think the issue is much more complex than the Right Reverend prelate is suggesting."
Premier reported earlier this month that the Christian charity Trussell Trust, which runs the majority of foodbanks across Britain, gave out more emergency food supplies in the six months to September this year than in 2014.