Nonrecursive 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 $k went outofbounds, there are no more valid iterations:
} while ($k >= 0);
}
my @a = ...;
my @b = ...;
my @c = ...;
nested_foreach { say join ' ', @_ } \@a, \@b, \@c;
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. base10) 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 rightmost 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 },
};
s/iter iterative recursive
iterative 1.86  71%
recursive 0.532 249% 

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