The main way in which we can argue that minimum sentencing is unjust is to say that different cases call for different punishments. It is, therefore, not really possible to maintain justice while setting out mandatory minimum sentences that must be adhered to in all cases.
The main problem with mandatory minimum sentences is that they do not account for the possible differences in cases. The law should not be so blind that it treats all people exactly the same. There should be room to be lenient for someone who has, for example, committed a crime out of desperation or for someone who has never been in trouble with the law before.
Minimum sentences are also problematic because they are often set too high. Our society rewards politicians who look tough on crime and so politicians push for higher and higher minimums. This makes the minimum sentences for many crimes be excessive.
Our mandatory minimum sentences are arguably too high and too inflexible. This means that, if we accept those claims, they are unjust.