The Canadian light-heavyweight needed surgery after he was knocked out by Ukrainian Oleksandr Gvozdyk this month.
Simone 'SiSi' God said the 41-year-old was recovering "in the private company of his family".
"Adonis is a world champion and is exhibiting that same determination in his recovery," she said.
"Despite recent reports being leaked to media, I wanted to clarify that Adonis is awake."
Stevenson, boxing's oldest and longest-reigning champion, was making his 10th WBC title defence when he was injured.
He suffered an 11th-round knockout during the light-heavyweight bout on 2 December, slumping after a flurry of punches from his opponent.
"Superman is a world champion and has demonstrated his strength in facing every obstacle he has ever faced," the statement continued.
"He is a legend in the eyes of his fans, and a man that demonstrates to his family daily that inner strength and love can change and redeem even the greatest of hardships."