The 29-year-old said the hair, believed to be part of the cow's hide, had come from a £3 packet of frozen mince bought at Iceland's Gosport store.
Ms Stock said Iceland had investigated and given her £30 in vouchers as an apology.
It's completely traumatised her now. She was in buckets of tears. She was enjoying it until she found that and burst out crying.
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Tuesday's weather for the west of the region
Tuesday's weather for the east of the region
The Government has previously described the new coin - which enters circulation on Tuesday - as "harder to counterfeit than ever before".