The 19-year-old attacker will stay with the Millers until January 17 and will be available to make his debut against Ipswich in the Sky Bet Championship on Saturday.
Barker's potential was highlighted by him signing a five-year contract in August with the Premier League side and he has been involved in a matchday squad on six occasions.
"He is an exciting young player," Millers boss Neil Redfearn said. "He represents a ball carrier who will go past players and make things happen.
"He is a goalscorer who is quite young in years but has had quite a lot of experience around the first team at Manchester City.
"They think that he is going to develop into a top player so for us to get him is a massive plus. It is a great deal for us, he is what we need. He has the ability to open sides up and he can create goalscoring opportunities and he can score goals. He will be a massive addition for us.
“What we need to do is whatever system we play, we have to free him up and get him running at the opposition.
"Once he starts going past people, he will start creating chances. He can finish, he has been a regular goalscorer for Man City under-21s, and this is the start of us changing the face of what we look like. We want to do this, it is the consensus of the technical board, and Brandon is the start."
