Perhaps this one is, what you are looking for?

C:\Daten\perl>cat match.pl
#!/usr/bin/perl
use strict;
use warnings;

my $var = 'Sensor30';

while (<DATA>) {
    print if /^>?\Q$var\E$/;
}

__DATA__
>Sensor30
>FooSensor30
> Sensor30
Sensor300
Sensor30
>Sensor3


C:\Daten\perl>perl match.pl
>Sensor30
Sensor30
[download]

Without a regular expression:

C:\Daten\perl>cat match.pl
#!/usr/bin/perl
use strict;
use warnings;

my $var = 'Sensor30';

while (<DATA>) {
    chomp;
    print "$_\n" if $_ eq $var or $_ eq '>' . $var;
}

__DATA__
>Sensor30
>FooSensor30
> Sensor30
Sensor300
Sensor30
>Sensor3


C:\Daten\perl>perl match.pl
>Sensor30
Sensor30
[download]

Thats what I was missing...Thank you!

I modified it a bit to include the space if it exists:

my $var = 'Sensor30';

while (<DATA>) {
    chomp;
    if (/^(>\s*)?\Q$var\E$/) {
    print "MATCH => $_\n";
    }

}

__DATA__
>Sensor30
>FooSensor30
> Sensor30
Sensor300
Sensor30
>Sensor3
[download]