I don't recall the Bible saying that only God can judge, Maybe you could point out what verse you are basing your question on so I can understand it.
Matthew 7:1-5
“Judge not, that you be not judged. For with the judgment you pronounce you will be judged, and with the measure you use it will be measured to you. Why do you see the speck that is in your brother's eye, but do not notice the log that is in your own eye? Or how can you say to your brother, ‘Let me take the speck out of your eye,’ when there is the log in your own eye? You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother's eye.
Luke 6:37
“Judge not, and you will not be judged; condemn not, and you will not be condemned; forgive, and you will be forgiven;
James 4:11-12
Do not speak evil against one another, brothers. The one who speaks against a brother or judges his brother, speaks evil against the law and judges the law. But if you judge the law, you are not a doer of the law but a judge. There is only one lawgiver and judge, he who is able to save and to destroy. But who are you to judge your neighbor?