Pretorius, who was born in South Africa but qualified for Wales on residency late last year, was selected in this season's RBS 6 Nations squad although he did not feature in games against Ireland, France and Italy.
The 27-year-old aggravated a shoulder problem playing for the Blues against Edinburgh earlier this month, and will be out until May.
In a statement, the Blues said: "Following consultation with the medical team, Pretorius underwent shoulder reconstruction surgery on Friday, which went well, and the Blues number eight is due to return to full training in May."
