Police are warning people to be on their guard after the woman called at Dawn Emery's home in Ingram Road, Holbeck and tried to give her baby daughter, Bethany, an injection.
The woman was wearing a blue nurse's uniform and carrying a needle box.
She had an NHS card and said she was there to give Bethany her immunisations – but Dawn, 27, was suspicious because Bethany only had her eight-week jabs last week.
She said she had to collect her other daughter, Rebecca, seven, from school – so the woman told her to make a new appointment with her doctor before leaving.
Dawn later called staff at the Thornton Medical Centre in Wortley, who said the woman, was not a registered nurse.
Dawn said: "It makes me feel sick just thinking about what could have happened. She could have injected her with something or snatched her when my back was turned.
"At first, I wasn't suspicious because she knew our names and she had an NHS card, which she flashed at me.
"But then she said she was there to give Bethany her immunisations, which I thought was strange because she only had them last week. I'd probably have let her in otherwise.
She looked like a real nurse; she even had a hypodermic needle box. She knew my name, she knew my daughter's name - it's freaky really.
"I don't think it was anything personal; I just think she's just out there targeting people with babies.
"My advice would be, don't let anybody in to do anything and just be cautious at all times.
Dawn described the woman as being 30 to 35 years old, with mousey-blond curly hair, and glasses. She was carrying a black handbag and small needle box.
Pam Wilson, practice manager at Thornton Medical Centre, said:
A police spokesman said: "At 2.45pm yesterday, police received a report of a suspicious incident involving someone claiming to be a nurse, calling at a property on Ingram Road, Holbeck. Police are currently making enquiries.
"Police would advise members of the public to be cautious if they receive any unexpected caller. If you do not know the person and are not expecting them, do not allow them into your home. Check with the organisation they claim to be from that they are genuine.
"Any caller with a valid reason to visit should be happy to wait outside whilst you check their details with the relevant authority."