Lazy solution causing the whole file to be slurped up front:

my @match = do {
    open my $fh, '<', $file or die "$!";
    grep /^$ARGV[0]\|/, <$fh>;
};
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If your file is large, it takes more effort.

my @match;
{
    open my $fh, '<', $file or die "$!";
    local $_;
    my $rx = qr/^$ARGV[0]\|/
    m/$rx/ && push @match, $_ while <$fh>;
}
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If I need the latter more than once, I'd probably factor it out:

sub grep_file {
    my ($rx, $file) = @_;
    my @match;
    local $_;
    open my $fh, '<', $file or die "$!";
    my $rx = qr/^$rx\|/
    m/$rx/ && push @match, $_ while <$fh>;
    @match;
};

my @match = grep_file($ARGV[0], $file);
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Makeshifts last the longest.