I can do
5 pieces (2K,3Q):
and this is clearly optimal, because
1 of the 5 pieces must be the black king. One must be the white which can only cover 3 squares leaving at least 15 for the remaining pieces. As obviously no piece can block more than 6 squares (a queen next to the opponent's king does 6) no fewer than 3 more pieces are needed.
Picture of solution.
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[FEN "Q2Q2/4k1Q1/8/3K4/8/8/8/8 w - - 0 1"]
The mating move would have been a pawn promotion: f7-f8=Q#
