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The 72-year-old, who played 104 times for Otago as well as 30 matches for the national side in the 1970s, was flown to Christchurch Hospital, where he is now in a stable condition.
In a social media post, Mr Robertson's daughter, Olivia, said it was suspected her father was hit by a car.
"Any information of a friend or family member that has arrived home last night with suspicious damage to their vehicle, then we ask you to please inform police.
"And if you are the person that left my father, an elderly man lying unconscious and bleeding out in the middle of the road, then shame on you ... and please we ask you to turn yourself in."
Sergeant Simon Matheson, of Queenstown police, said the incident occurred while Mr Robertson was taking his bins out to the road about 9pm.
Police wanted to hear from anyone who was in the Hunter or Mooney Rd area, in Dalefield, about that time, he said.
• Contact: Police (03) 441-1600, Crimestoppers 0800 555 111