Quick note -- it's not actually working so well yet, even disregarding abbreviations. Consider the following input:

This is a sentence. This is another sentence. This is a third
sentence, which also happens to be spanning a line. This is a
sentence as well... I think. This is an abbreviation, cf. the
list posted on Perlmonks. This is a sentence; this is the last
sentence.
[download]

This produces:

This is a sentence.
This is another sentence.
This is a thirdsentence, which also happens to be spanning a line.
This is asentence as well.
I think.
This is an abbreviation, cf.
Perlmonks.
This is a sentence;
[download]

As opposed to:

This is a sentence.
This is another sentence.
This is a third sentence, which also happens to be spanning a line.
This is a sentence as well... I think.
This is an abbreviation, cf.
the list posted on Perlmonks.
This is a sentence;
this is the last sentence.
[download]

Note how the third and fourth one are missing a space and how lowercase characters following semicolons or periods aren't handled correctly.

Try the following -- add a space in your loop, and use a lookahead assertion to take a peek at what's following a period or colon:

#!/usr/bin/perl

use feature qw/say/;
use strict;
use warnings;

my $s;
my @arr;

while(<>) {
  chomp $_;
  $s .= $_ . " ";
}
@arr = $s =~ m/[A-Z].+?[.;](?=[^.;][A-Z]|\s*$)/g;
foreach (@arr) {
    say;
}
[download]

This produces:

This is a sentence.
This is another sentence.
This is a third sentence, which also happens to be spanning a line.
This is a sentence as well...
I think.
This is an abbreviation, cf. the list posted on Perlmonks.
[download]

As you can see, it's not perfect -- it still splits if you have e.g. a run-on sentence followed by an "I", or in fact any uppercase word, e.g. a proper noun --, but it mostly handles abbreviations (arbitrary ones, even). What I'd do to fix the remaining edge cases is add another processing step after the regex where you loop over @arr, check if each element ends with a known abbreviation, and join that element with the next one if so.