The gesture left workers at the Ammanford food bank “blown away”, said worker Paul Kennedy.
He said they expected to help at least 100 people over the next three weeks, the majority of whom have families.
The delivery has also given them “peace of mind that we can definitely manage, no matter how many come through the door”.
Mr Kennedy said they were called by Tesco on Thursday to say a delivery had been put through their system for the food bank.
“The person who phoned through said it was at least £100 worth of food, which we were amazed at – it was very generous,” he said.
“When the delivery arrived the food bank manager asked which crates were ours and was told ‘they’re all for you’.”
He said whoever bought the food had looked at their website to see what items they needed.
“We were blown away. It’s the largest donation by an individual to our food bank.
“Universal Credit comes into the area today and, with Christmas as well, it’s by far our busiest time.
“We just want to express our gratitude really on behalf of our clients because, while it helps us as a food bank, that help goes straight to the clients.”