This should work for your needs:

my $range = qr/^
(
 (?:                               # first 3 octets:
  (?: 2(?:5[0-5]|[0-4][0-9])\. )   # 200 - 255
  |                                # or
  (?: 1[0-9][0-9]\. )              # 100 - 199
  |                                # or
  (?: (?:[1-9][0-9]?|[0-9])\. )    # 0 - 99
 )
 {3}                               # above: three times
 
(?:                                # 4th octet:
 (?: 2(?:5[0-5]|[0-4][0-9]) )      # 200 - 255
  |                                # or
 (?: 1[0-9][0-9] )                 # 100 - 199
  |                                # or
 (?: [1-9][0-9]?|[0-9] )           # 0 - 99
)
 
$)
/x;
print "OK\n" if ($ip =~ /$range/);
[download]

Update:
Changed (?: [0-9][0-9]? ) to (?: [1-9][0-9]?|[0-9] ) so that it won't accidently match an octet with only 2 or more zeros or an octet with leading zero (i.e. 00.0.0.0 or 192.186.0.01)
Now this will only match addresses from 0.0.0.0 to 255.255.255.255 (assuming the address in $ip is already chomped)