my %hash;
my $condition = sub { ! exists $hash{key} };

# and later on use it as
if ($condition->()) {
    print "'key' does not exists in \%hash\n";
}
[download]

Nope, because when you put variables inside double-quoted strings, they get interpolated. This is something you should already know, as you would use it in common statements such as print "The value is $value. The dog's name is $dog{name}. The third element is $elements[2]."

See this:

use strict;
use warnings;

my %hash = (
    foo => "bar",
    bar => "baz"
);

sub testAndExec {
    my $cond = shift;
    if (eval $cond) {
        print "This is executed!\n";
    } else {
        print "Not executing this time.\n";
    }
    print "But there was an error:\n    $@" if $@;
    print "\n";
}

my $exeif = "!exist $hash{foo}";
print "Double quotes, existing key: <$exeif>\n";
testAndExec $exeif;

$exeif = "!exist $hash{foo}";
print "Double quotes, existing key: <$exeif>\n";
testAndExec $exeif;

$exeif = '!exists $hash{bar}';
print "Single quotes, existing key: <$exeif>\n";
testAndExec $exeif;

$exeif = '!exists $hash{baz}';
print "Single quotes, non-existing key: <$exeif>\n";
testAndExec $exeif;
[download]

Output:

Double quotes, existing key: <!exist bar>
Not executing this time.
But there was an error:
    Can't locate object method "exist" via package "bar" (perhaps you 
+forgot to load "bar"?) at (eval 1) line 1.

Double quotes, existing key: <!exist bar>
Not executing this time.
But there was an error:
    Can't locate object method "exist" via package "bar" (perhaps you 
+forgot to load "bar"?) at (eval 2) line 1.

Single quotes, existing key: <!exists $hash{bar}>
Not executing this time.

Single quotes, non-existing key: <!exists $hash{baz}>
This is executed!
[download]

Update: fixed a logical flaw spotted by AnomalousMonk. Thanks.