The woman contacted security staff after her waters broke at the Intu Lakeside Shopping Centre in Essex.
Although an ambulance was called and arrived quickly, the baby girl was delivered before they got to the scene on Thursday evening.
Paul Lancaster, regional manager of Intu, said the woman had been in "distress" but was now "doing well".
Staff at Primark provided towels for the woman on the second floor of the shopping complex.
She was screened off as she gave birth to her daughter, whose name is understood to be Deborah.
"In 23 years we've never had a birth at the site," said Mr Lancaster. "Plenty of ladies have broken water and gone off to hospital and no doubt a couple of babies have been conceived here.
"It all happened rather quickly before the ambulance could get there. They responded really quickly.
"We didn't think it was immediately going to happen but the baby was born on the spot."
A shopper ended up giving birth outside a Primark store after she suddenly went into labour.