Kirsty Hensby of Devon, South West England, picked up a prescription from the supermarket after her three-month-old daughter Summer developed a rash.
The 22-year-old veterinary nurse, whose fiance Simon is a lorry driver, was given a prescription for 3ml of penicillin three times a day.
However the worker at the in-store pharmacy at her local Tesco labelled the bottle with a dose of 5ml.
After Miss Hensby began administering the drug, Summer was repeatedly sick. The worried mother called NHS Direct, where a doctor told her that she should continue giving her daughter the antibiotics.
When she went back to her GP four days later, Miss Hensby realised she had been giving Summer the wrong dose.
'The doctor had written three spoons of 3ml penicillin three times a day yet I had been giving Summer 5ml, 66 per cent more than a baby is supposed to have.
'The doctor said that a child had to be at least six years old to be given a 5ml dose and that giving that to a baby was a terrible risk.'
Miss Hensby immediately rang the pharmacy. 'The assistant said "Oh my God" and admitted straight away that they had made the mistake.'
Mercifully, Summer is showing no ill-effects from the overdose, but her angry mother has been given an apology and offered compensation by the supermarket.
Tesco has previously attracted criticism from the pharmaceutical industry over its policy of recruiting lower-paid chemists directly from abroad.
Earlier this year a grandmother died after a pharmacist at another branch of Tesco gave her the wrong pills while working ten-hour shifts without a break, Daily Mail reported.
Miss Hensby was later contacted by an area manager.
'He told me that the pharmacist was a locum and that they were going to monitor his performance. After a week they came back and said they would not be using him any more.'
Doctors say there is no sign of damage to Summer, but she must be regularly monitored in case of liver and kidney damage.
Tesco has offered her mother £600 compensation, but she says that is nowhere near enough for the trauma she has suffered.
'It was as though I was complaining about a can of baked beans being past their sell-by date, rather than the health of my daughter.
'I have lost one child already and I couldn't bear the thought of losing another one.
'You don't expect a company that size to employ people who don't know what they're doing.'
The pharmacist, who as a locum was not directly employed by Tesco, now faces an investigation into his competence by the Royal Pharmaceutical Society of Great Britain or even criminal charges.
A Tesco spokesman said: 'We have very high standards in our pharmacies and rigorous procedures for dispensing medicines.
'We have investigated this incident fully and have been in touch with the customer to apologise.'