Mum-of-two Rosey Hughes was visiting Costa Coffee in Stretford Mall when she says she was approached and asked to stop feeding baby Zoe as another customer had complained.
Rosey, who was at the store with her friend Jenny Appleby and says she was feeding 'discreetly', refused to leave the coffee shop until she had finished.
Jenny then took to the company's Facebook wall to complain about the incident on behalf of her friend, writing, 'Just thought every breastfeeding Mummy should know to avoid Stretford Mall, Manchester Costa Coffee.'
'A member of staff approached my friend while we were having coffee and she was discretely breastfeeding her 5 month old baby girl. She was asked to cover the baby up as she'd had a complaint from a customer saying they were offended.'
'I was lead to believe that Costa Coffee was a breastfeeding friendly environment, clearly I was wrong. Truly shocked and disappointed.'
Speaking after the incident, Rosey explained, 'We were just sat as normal having a coffee and we were told someone had complained about me.'
'I was asked to cover up but I was no more exposed than I usually am when feeding. I was really taken aback by it.
'It was a bit of a shock and I went a bit quiet but Jenny spoke up for me and told the staff that they had no right to ask that of me.'
She added that while she was a 'confident breastfeeder', the incident had taken her by surprise.
'I've never had any issues anywhere before. I was surprised that the staff acted because of a complaint with one customer.
'Surely the staff should have told the customer just to sit elsewhere if they weren't comfortable? I pretty much ignored her and carried on. I was doing nothing wrong.'
Rosey with her two children, Zoe and Daniel
Costa responded quickly to Jenny's post, and a spokesperson for the brand told the Manchester Evening News, 'Mothers bring in children of all ages to Costa and they are always warmly welcomed by us.
'We have always been very happy for mothers to breastfeed in our stores and for all those who prefer a more private area, we offer baby changing facilities.'
'Costa is renowned for its family friendly environment and is the perfect place for mum's to relax with their children.
'Our staff will also warm bottles for mothers, deliver drinks to their tables and go out of their way to accommodate families.
'We have reached out via our social channels to speak to the customer in question and have launched an investigation into this matter.
'We'd like to assure customers that this incident does not reflect our breastfeeding friendly policy.'