splice is the preferred tool in Perl for managing chunks of arrays. Consider:

use strict;
use warnings;

my $test = '';

while (<DATA>) {
    if (! /^\d+$/) {
        $test .= $_;
        next;
    }
    
    chomp;
    my $n = $_;
    my @words = split /\s+/, $test;
    my @lines;
    
    # Use splice to pull out the desired lines
    push @lines, [splice @words, 0, $n] while @words;
    
    print "@$_\n" for @lines;
}


__DATA__
A huge string separated by lots and lots of words that I'd like to bre
+ak up
into n shorter strings of length y. This is stored in a __DATA__ secti
+on to
make a stand alone test program.

Note that lines containing only a number provide an 'n' like the 10 on
+ the
following line.
10
Note too that you can add more text that will be added and processed b
+y any
subsequent 'n' lines.
12
[download]

Prints:

A huge string separated by lots and lots of words
that I'd like to break up into n shorter strings
of length y. This is stored in a __DATA__ section
to make a stand alone test program. Note that lines
containing only a number provide an 'n' like the 10
on the following line.
A huge string separated by lots and lots of words that I'd
like to break up into n shorter strings of length y. This
is stored in a __DATA__ section to make a stand alone test
program. Note that lines containing only a number provide an 'n' like
the 10 on the following line. Note too that you can add
more text that will be added and processed by any subsequent 'n'
lines.
[download]

which nicely gets rid of all those nasty C style for loops with their tricksy conditions and increments, and also removes the need for fussy slices and error prone indexes.

Perl's toolbox is pretty extensive and for some reason splice is often overlooked - it's worth knowing about.