Dos Anjos sustained the injury a few weeks before his title fight against Anthony Pettis at UFC 185 on March 14.
Instead, dos Anjos has decided to undergo a 90-day rehabilitation programme.
However, dos Anjos' manager Ali Abdel-Aziz has confirmed that the 30-year-old will need to have his nose surgically repaired.
"Rafael is on his way to Brazil right now to do a victory tour," Abdel-Aziz told ESPN. "He will do 90 days' rehab before training. Next Thursday, he is getting nose surgery. He fought [Pettis] with the right side [of his nose] completely closed and could breathe only 70 percent out of the left side."