How about the following solution?
% 100-by-100 sample matrix
Zin = peaks(100);
Zin = Zin - min(Zin(:));
% Example of polygon
pgon = polyshape([10 10 80 30], [10 30 30 10]);
% Create logical index which indicates inside/outsize the polygon
[colGrid,rowGrid] = meshgrid(1:size(Zin,2),1:size(Zin,1));
idx = isinterior(pgon,[colGrid(:),rowGrid(:)]);
idx = reshape(idx,size(Zin));
% Set elements inside the polygon to 0
Zout = Zin;
Zout(idx) = 0;
% Show the result
figure
subplot(2,2,1)
contourf(Zin)
title('Original','FontSize',14)
colorbar
subplot(2,2,2)
plot(pgon)
xlim([1 100])
ylim([1 100])
box on
title('Polygon','FontSize',14)
subplot(2,2,3)
contourf(Zout)
title('Result','FontSize',18)
colorbar
