Non-recursive solution

For completeness, here's a solution that does not use a recursive subroutine:

sub nested_foreach(&@) {
  my $code = shift;
  my @indices = map { 0 } @_;  # First set of indices is all zeroes
  my @sizes = map { scalar @$_ } @_;  # Cache array sizes (optional)
  my $k;
  
  do {
    # Determine the array elements corresponding to the current set
    # of indices, and pass them to the closure:
    $code->( map { $_[$_][$indices[$_]] } 0..$#_ );
    
    # Determine the next set of indices:
    for ($k = $#_; $k >= 0; $k--) {
      $indices[$k]++;
      if ($indices[$k] < $sizes[$k]) { last; }
      else { $indices[$k] = 0; }
    }
    
    # If $k went out-of-bounds, there are no more valid iterations:
  } while ($k >= 0);
}

my @a = ...;
my @b = ...;
my @c = ...;

nested_foreach { say join ' ', @_ } \@a, \@b, \@c;
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The "Determine the next set of indices" step may seem a little complicated at first sight, but it becomes more intuitive if you think of the @indices array as an integer number (with each element representing a digit), and imagine that we want to "increment" that "number" by 1. It's not a decimal (i.e. base-10) number, but rather one where each digit can have a different base (i.e. the sizes of the input arrays) - but that doesn't really change anything.

Incrementing the "number" by 1 works just like the integer addition (here with an addend of 1) that you were taught back in primary school: Start with the right-most digit; increment it; if it's still within the valid range of digits then you're done; if instead it went above the limit then wrap it around to zero, "carry the one", and repeat the same steps with the next digit to the left.

Update:

Performance comparison

Interestingly, my iterative solution seems to be significantly slower than BrowserUK's recursive solution, at least when running on my PC and with various different numbers/sizes of input arrays I tried:

sub nested_foreach(&@) {
  ... # see above
}

sub nForX(&@) {
    ... # see BrowserUK's post
}

# my @size = (500, 900);
# my @size = (5, 5, 5, 5, 5, 5, 5, 5);
my @size = (100, 4, 75, 23);
my @AoA = map { [map { chr($_+64) x int(rand(10)) } 1 .. $_] } @size;

cmpthese -10, {
    iterative => sub { nested_foreach { join("", @_) } @AoA },
    recursive => sub { nForX { join("", @_) } scalar @AoA, @AoA },
};
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          s/iter iterative recursive
iterative   1.86        --      -71%
recursive  0.532      249%        --
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