The comments came after RTÉ reported some women living at the asylum centres had become prostitutes as they are given less than €20 a week by the State.
The justice minister has ordered a report on the situation from the Reception and Integration Agency, which is responsible for providing accommodation and services for asylum seekers while their applications are processed.
Ms Fitzgerald said people should be careful not to stigmatise asylum seekers.
“I did find and I do find those reports shocking. I certainly don’t want to see any woman in Ireland feeling that the only option for her is prostitution in order to look after her family.
“First of all, I would be very concerned that there would be any targeting of the women who are in direct provision,” she said.
“I would be concerned as well about any stereotyping that might take place in relation to those women in any media reports.
“We are talking about a vulnerable group of women and I certainly don’t want to see them further stigmatised,” the minister said.
On calls by former US president Jimmy Carter, and others, to criminalise the buying of sex, Ms Fitzgerald also said she would be bringing legislation to Cabinet in the near future.
Ms Fitzgerald said she had been watching how Scandinavian countries had handled the issue.
The justice minister also attacked claims by Fianna Fáil leader Micheál Martin that the next Garda commissioner would be selected under a cloud because Taoiseach Enda Kenny had refused to outlay the circumstances leading up to the sudden resignation of former commissioner Martin Callinan.
Ms Fitzgerald said she disagreed with the remarks made by Mr Martin in an Irish Examiner interview and the next commissioner would not be compromised by the events leading up to the departure of Mr Callinan from his post in March after Mr Kenny had sent a senior civil servant to the then commissioner’s house to express concern at an unfolding Garda station telephone taping controversy.
“I don’t accept what Micheál Martin has said,” Ms Fitzgerald said.