Carena initially studied engineering at the Instituto Tecnológico de Buenos Aires, then studied philosophy at the University of Buenos Aires, and finally received her diploma in physics from the Instituto Balseiro in Bariloche, Argentina in 1985. That same year, at the encouragement of Robert Peccei, Carena and her husband, Carlos Wagner, were offered positions at the University of Hamburg and at the DESY Laboratory in Hamburg, Germany. Carena received her PhD in high energy physics from the University of Hamburg in 1989.