White wasn't selected in Robbie Deans' original 25-man squad last month but had been tipped for a call up when six additional players are selected this Tuesday.
The 22-year-old has enjoyed a superb season in Canberra and it was a surprise to see him overlooked in the first place.
White became the Brumbies' youngest ever captain in their convincing win over the Rebels as they clinched the Australian Conference on Friday but he lasted just nine minutes of the match before being hit with a shoulder injury.
Scans have since revealed a small fracture, with an estimated four-week recovery time meaning he will miss The Lions series but could still return in time for the Super XV finals.
''It's a better result than what I had expected and I'm looking forward to being involved with the Brumbies towards the tail end of the season,'' said White, who has struggled with shoulder problems for the past two seasons.
''It is a good result considering where I have been with my shoulder and how far surgery can set you back.
''All my focus will be on getting this right for the next game against the Western Force in a month's time.''