I believe VCFtools can do that. It's an example in vcf-annotate for designing a custom filter for use with the --filter option (click the "Read even more" link on the documentation). The filter:

# Annotate INFO field with SINGLETON flag when one and only one sample is different from the reference
{
    header   => [
        qq[key=INFO,ID=SINGLETON,Number=0,Type=Flag,Description="Only one non-ref sample"],
    ],
    tag      => 'FORMAT/GT',
    name     => 'Dummy',
    desc     => 'Dummy',
    test     => sub {
        my $nalt = 0;
        for my $gt (@$MATCH)
        {
            my @gt = $VCF->split_gt($gt);
            for my $allele (@gt)
            {
                if ( $allele ne 0 && $allele ne '.' ) { $nalt++; last; }
            }
            if ( $nalt>1 ) { last; }
        }
        if ( $nalt==1 ) { $$RECORD[7] = $VCF->add_info_field($$RECORD[7],'SINGLETON'=>''); }
        return $PASS;
    },
},

I would use awk to find one sample having a genotype!="0/0"

 gunzip -c my.vcf.gz |
awk -F ' ' '/^#/{print; next;} {n=0; for(i=10;i<=NF;++i) { if($i!="." &&  index($i,"0/0")==0) n++;} if(n==1) print; } '

change the test according to your needs.