I don't know offhand which template modules support that mechanism, but maybe Reverse Callback Templating might be of interest to you.

Unless someone else has come up with exactly the templating scheme you are using (which is rather unlikely), you are going to have to adjust your template documents somewhat. However that needn't be much and there are plenty of templating engines around that are happy dealing with plain text. For example, with HTML::Template you could:

use strict;
use warnings;
use HTML::Template;

my $str = <<STR;
For example, if user defines in a template a string "%section_10%" I r
+etrieve
value "10", make a mySQL query to select some text from row with id = 
+10 and
then replace text with query result "<!-- TMPL_VAR "section_10" -->".
STR

my @db = ('', qw(the quick brow fox jumps over the lazy dog should suf
+fice));
my $template = HTML::Template->new (scalarref => \$str);
my %usedParams = map {lc ($_) => 1} $template->param ();
my @usedIds = map {m/section_(\d+)/; $1} keys %usedParams;

$template->param ("section_$_" => $db[$_]) for
    grep {defined $_ && length $db[$_]} @usedIds;

print $template->output ();
[download]

Prints:

For example, if user defines in a template a string "%section_10%" I r
+etrieve
value "10", make a mySQL query to select some text from row with id = 
+10 and
then replace text with query result "should".
[download]

Which recognizes your variable pattern, extracts the index, performs the look up, then reconstitutes the variable to apply the value in the template.

Not exactly as you want, but Template::Toolkit allows you to make SQL query directly from your template.