St. Gallen police said the incident happened early Sunday in the northeastern Swiss town of Rorschach.
Police said the suspects - a married couple and their 10-year-old daughter - are accused of attacking the taxi's 60-year-old driver before stealing his car and driving erratically to a nearby town.
Their alleged taxi ride ended when the family crashed down the side of a driveway. Police say officers detained them as they fled.
Police said the 38-year-old father "was not in a fit state to drive" and had no license. The girl and the taxi driver were injured and required medical treatment.
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