A Brisbane mother has been charged with supporting terrorism after being arrested while trying to leave Australia with her four young children.

The 29-year-old woman was charged as a result of a counter-terrorism operation that focuses on foreign incursions, an Australian Federal Police spokeswoman said.

Detectives from the NSW joint counter-terrorism team stopped the woman at Sydney airport about 8.30pm on Saturday, trying to board an international flight with her children.

The AFP could not comment on reports the woman was carrying cash and equipment intended for her husband, who is in war-torn Syria.

Three properties have been searched in relation to the operation, two in Sydney and one in Brisbane.

The woman has been charged under the Crimes (Foreign Incursions and Recruitment) Act 1978.

"She was charged with supporting incursions into a foreign state, with the intention of engaging in hostile activities," the AFP spokeswoman said.

She was granted strict conditional bail and will appear in Sydney's Downing Centre Local Court on June 2.

AAP