$data =~ s/$m/$prepared_string/s;

$data =~ s/\Q$m\E/$prepared_string/s;

#!/usr/bin/perl
use strict;
use warnings;

local $/ = undef;
my $data = <DATA>;

{
  my $out='';
  while($data =~ s|\A(.*?)<Text>([^<]*)</Text>||s)
  { $out .= $1.prepare_string($2); }
  $data=$out.$data;
}

print $data;

## subs ##
sub prepare_string {
  my $string = shift;
  my $chunk_size = 10;
  my $prepared_string;
  for (my $i = 0; $i <= length($string); $i+=$chunk_size){
    my $part = substr($string, $i, $chunk_size);
    $prepared_string .= "<Text>$part</Text>\n";
  }
  return $prepared_string;
}

__DATA__
<Feld><Text>Hallo liebe Perl-
Geme(i)nde.

diesmal mit leerzeile
</Text></Feld><Sig>
abc</Sig>
<Text>V[iel]e Grüße
leo11</Text><Text>ps.: schönen abend</Text>