The purse snatching took place during Barbara's first night in town in the San Telmo neighborhood, ABC News reports on its Web site.
The Secret Service would not comment on the robbery, and the First Lady's office said they would not comment on any personal trip made by the Bush daughters, the ABC News report said.
Barbara and her twin sister, Jenna, will turn 25 on Saturday.
This wasn't the only troubling incident on the twins' trip to Argentina: a Secret Service agent on the advance detail got into an altercation with someone after a night out and was badly beaten, according ABC News. The incident, described as an attempted mugging, happened while the agent was spending time on his own, the Secret Service told ABC News.