The luckless Hurricanes back has endured a torrid 18 months with injuries, including a dislocated left shoulder and broken foot.
His most recent setback - dislocating his right shoulder in this month's 25-24 Test win over South Africa - will keep him out until at least next April.
The Springboks match was Milner-Skudder's third Test of 2017, having played in the reverse fixture in Albany and against Argentina in New Plymouth.
Milner-Skudder posted on social media that the operation had gone well and recovery should be between six and seven months.
