To reduce surprise, the function should return true if the number is valid, and false otherwise, which is the other way round.

There's no need to backslash a space in regular expressions. Moreover, there's no need for a substitution in this case, transliteration does the same job (and is simpler and faster).

There's a pattern in the computation of the sum which could be expressed by a for loop.

See my version below:

sub check_abn {
    my ($number) = @_;
    $number =~ tr/ //d;
    return if 11 != length $number;

    my $sum = 0;
    $sum += (2 * $_ - 1) * substr $number, $_, 1 for 1 .. 10;
    $sum += 10 * (substr($number, 0, 1) - 1);
    return $sum % 89 == 0
}
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