Not answering your query, but running min every time through the grep is likely to be wasteful if you are dealing with large arrays. It might be better to find the minimum once first.

$ perl -Mstrict -Mwarnings -MList::Util=min -E '
my @NI = ( 1, 1, 3, 4 );
my @NI_index = do {
   my $min = min @NI;
   grep { $NI[ $_ ] == $min } 0 .. $#NI;
   };

say qq{@NI_index};'
0 1
$
[download]

I hope this is of interest.