Speaking at a conference organised by crime-reduction charity Nacro Cymru, Edwina Hart said custody should be a "last resort" but when it is necessary young people should be held in small units close to their homes.
"This will involve a greater cost, but you have to look at the long-term benefits," she said.
In recent years, the Youth Justice Board, which manages custody for under-18s in England and Wales, has cut the number of places it uses at local authority-run centres.
Howard Williamson, a member of the Youth Justice Board and Young People Now columnist, told the conference the problem with local authority-run centres was that they cannot provide the same facilities as bigger centres.
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