Officials allegedly told Emma Mitchell, 32, it would 'cause an uproar' in the multi-cultural building if she fed her 19-week-old son Aaron.
Staff instead suggested that she used the public toilets in a shopping centre nearby.
The angry mum said she was left feeling 'humiliated and intimidated' after the events at Access Oldham's civic centre offices.
Mrs Mitchell had asked staff if she could feed crying Aaron facing the wall in an empty corner of the room, but claims she was told by a female receptionist, 'Oh no, we don't allow that here. We've had many complaints.'
Emma said: 'There were only five or six people in the room, mostly Asian like her.' She claims another member of staff later told her: 'You've caused an uproar in there.'
The Metro reports the Labour councillor Shoab Akhtar as initially saying that the office 'wasn't suitable" for breastfeeding': 'Unfortunately there are no breastfeeding facilities available at Access Oldham based at the civic centre, nor are there any public toilets or baby-changing facilities. There is no requirement to provide such facilities at Access Oldham and we are committed to make the best use of the limited space available to provide facilities and meeting rooms.'
But Mrs Mitchell's local paper, The Saddleworth news, later reported that Shoab Akhtar had issued an apology on behalf of the council, saying:
'Ms Mitchell's disappointing experience has highlighted the need to make all our staff fully aware of our policy and our legal requirements. All staff will be trained in the coming days to ensure this never happens again.'
He continued: 'As previously stated, Access Oldham does not have dedicated breastfeeding facilities available, however staff are now aware that they should make every reasonable effort to assist a mother's need to breastfeed – whether she requests the use of a private room or otherwise.'
Emma Mitchell said: 'I was doing one of the most natural things that a mum can do. Everywhere you hear 'breast is best' and I believe it's the best thing for your child, so why wouldn't I be allowed to do it?"
What do you think? Do you think mums should be allowed to breastfeed anywhere, as and when their baby needs a feed?