"It certainly was never my intention to be disrespectful or demeaning to anyone in any way. I realize my costume hurt and offended people and I truly apologize," Hough said on Twitter.
Though cast member Laverne Cox called the incident "really sad," Aduba herself had yet to comment on the costume until Thursday.
"I think maybe it was an unfortunate event, but she apologized and I feel like we can all move on," Aduba told E! News.
Hough's brother Derek made a similar statement last month.
"She is just beyond beside herself. She's so apologetic. She's so so sorry," Derek said. "Obviously, it wasn't her brightest moment in her life, but hopefully we can move on."