The 26-year-old Burkina Faso-born Montpellier star - who also suffered an ankle injury during France's wooden spoon Six Nations campaign - will be replaced by Clermont's Damien Chouly for the remainder of the tour.
Ouedraogo came off in the 38th minute of Saturday's 23-13 loss to the All Blacks in the first of the three Test series.
Chouly, capped nine times but who was dropped from the Six Nations squad despite not playing a single minute of the opening two defeats, is unlikely to play in next Saturday's second Test in Christchurch.
France coach Philippe Saint-Andre was, however, able to give more reassuring news on centre Gael Fickou, whose shoulder problem has been resolved and he should be fit to play, if selected, against the Auckland Blues on Tuesday.