The 17-year-old midfielder completed his move to the League Two outfit on Thursday and will remain with the Bulls until 2 January 2010.
"It is a good opportunity for him to go on loan just now," McLeish told Birmingham's website. "I think that will be good for him playing at a senior level every week. I am sure he will do well.
"It will sharpen him up and it will toughen him up as well."
Earlier this year Mutch signed a professional contract with Blues and McLeish has nothing but praise for the way the youngster coped with last season's injury set back.
He added: "To come through that, that kid, to do what he's done, sit in a wheelchair for two or three months - incredible.
"He has got to slow down as well because he's come back from a potentially career-threatening injury."