Januzaj was one of the few players to shine during the first half of Moyes' debut season, but he has found himself out of the Manchester United first team of late.
The 19-year-old was an unused substitute against Olympiacos and West Ham while he did not even make the match day squad for Tuesday's Manchester derby.
But Moyes fears he may burn the teenager out unless he gives him some rest as the midfielder has already played 29 times this season.
"Adnan has played an incredible amount of games for a 19-year-old," the United boss said.
"We have to be mindful of that. We have seen signs in training that we have to be careful what we do with him.
"But he is a great talent. He is someone we know will go a long way at United. But we are just being careful with him. We have to do the right things and he has played a lot of football."
Januzaj, who moved to United from Anderlecht in 2011, signed a new five-year contract at Old Trafford last October after he broke into the first team.