The family of a 22-year-old South Australian woman accused of being a member of the Islamic State terrorist group has told African community leaders in Adelaide they are shocked by the woman's arrest.

The woman, who can't be identified for legal reasons, has been charged with being a member of a terrorist organisation after being arrested by Federal Police outside a TAFE college in Adelaide's west on Tuesday.

The president of the Federation of African Communities Councils, Joseph Masika, had a meeting with the woman's family in Adelaide today.

Dr Masika said family members were devastated.

"They're still coming to terms with what happened and how it happened and also to see how they can continue to be part of the society," he said.

"They don't want to be labelled as ... supporting terrorism. They are good people."

The woman appeared in the Adelaide Magistrates Court briefly yesterday afternoon, and her lawyer Craig Caldicott indicated his client would be pleading not guilty.

Speaking on ABC radio in Adelaide this morning, Mr Caldicott said the charge under Commonwealth anti-terrorism law carried a presumption against bail and it was likely his client would remain in custody for some time.

"At the moment with the backlog in trials, because this will end up in the District Court, it may be the middle of next year or the end of next year, so she could be in custody for about 18 months," he said.

At a media conference held on Tuesday, AFP assistant commissioner Ian McCartney said the woman had come to their attention when she attempted to leave Australia in July last year.

Police said they would allege the woman cultivated a relationship with Islamic State online and pledged her allegiance.

Dr Joseph Masika has known the 22-year-old woman since 2009. ( ABC News: Michael Coggan )

Dr Masika said he had known the 22-year-old woman since 2009, when she arrived in South Australia as a refugee, and she had been a student at an Islamic college before studying nursing.

From the perspective of African community members, Dr Masika said there had been no indication the woman might have been radicalised.

"She was still engaging as usual with the family and also with the community," he said.

Asked whether there were general concerns among Adelaide's African community about young people being radicalised, Dr Masika said: "We don't know anyone who has been radicalised, who is in process of being radicalised, and that's why it's come as a surprise."

Dr Masika has also appealed to the media to respect the privacy of the woman's family.