Spain forward Costa suffered the injury in an accidental clash in training and will become the third Chelsea player to wear a mask this season after Cesar Azpilicueta and Nemanja Matic.
"Diego got in a duel on the pitch, got his nose broken," Hiddink told a news conference on Friday.
"It was one of the youngsters in the academy, we like them to participate in the game. Diego put his nose on the back of the player and was very unlucky.
"His nose was broken, but he will return today, he will have a mask on. We are a team of a lot of masks -- we're a Zorro team. Azpi (Cesar Azpilicueta), Matic and now Costa."
Zorro was a fictional black-clad hero who sported a black mask in books, tv programmes and films.
Hiddink said Costa's fitness ahead of Saturday's home Premier League clash with Newcastle United (1730) will be monitored.
"He will come back in the hotel later. It was just a very small incident, it was nothing. I hope, I'm not sure, but I think he will be available."
Chelsea have drawn six of the eight Premier League matches since Hiddink returned to the club after Jose Mourinho's dismissal and the Dutchman said that "while being unbeaten sounds good, everybody wishes we had more wins".
Defender Kurt Zouma has been sidelined for the rest of the season and will miss the European Championship in his home country after surgery on a knee injury suffered against Manchester United last weekend.
"It is real shame Zouma will be out for so long, especially as he was in good form and the Euros in France are coming up," Hiddink said.
(Reporting by Justin Palmer, editing by Ed Osmond)
