The 16-year-old is the second youngest player to play for Blues after Trevor Francis, having appeared in two games in the Carling Cup this season.
"He's dynamite as a prospect. He's got quick feet and is exciting to watch, said Brewers manager Paul Peschisolido.
"We didn't think it would be a possibility to bring him here but Alex McLeish [Blues boss] has been brilliant.
"He feels that Burton Albion is the best place to go for him.
"I know that he had League One clubs interested in him.
"He'll be schooled properly here and I'm delighted that we've got him in."
Redmond, who has also represented England at Under-16 level, was 16 years and 173 days old when he played for Blues against Rochdale in August.
Source: BBC Sport
Source: BBC Sport