''Put it in here" seems correct to me. It makes sense if the box is close to you. Alternatively you could say "Put it in there", if the box is further away from you.

Hi Helen, Because you want the cat to be put in the box, you need to say "put the cat in the box", otherwise it could be implying that you want the cat to be put on the box, or next to the box. When you say come here you are demonstrating where you want the person to go with your body. When you say go there you are pointing or psychically demonstrating where you want the person to go. If the place was further out you would have to say go to Sydney, or go to Bangkok because you can not psychically demonstrate where you want the person to go. If you said to a friend over the phone come here you are assuming that the friend knows where here is. If the preposition is known then you can omit it.

Hi, Mojave! But as I say, there're many expressions where there are no preposition words before 'here'. For instance, if I say to a child, 'Come here.' instead of 'Come to here'. What do you say?

You would normally say "Put it in here". But if you specifically point to the inside of the box, you could say "Put it here".