Wiggins, who became the first Brit to secure the yellow jersey in the elite race two years ago, has taken a backseat to Chris Froome.
The 29-year-old will lead the team as he attempts to successfully defend his title following triumph in Paris last year.
"It was a very tough decision," Brailsford told Sky Sports News. "Bradley's been a great champion, but ultimately you've got to look at the facts as they stand now.
When asked about Wiggins's status within the team, Brailsford said: "We'd like to think that there's a future for Bradley."
The 34-year-old will compete in next month's Commonwealth Games in Glasgow.