Prozac can be taken either way. I found this article online and summed it up below:

Drugs such as lurasidone, sertraline, vilazodone, and ziprasidone are better absorbed when taken with food.

It is said that for the most part antidepressants (including Prozac) can be eaten on a full of empty stomach. MAOIs require that you don't eat food with thyramine. Vilazodone is an exception.

Antipsychotics except ziprasidone (Geodon) and lurasidone (Latuda) can be taken either way, the above better absorbed with food.

For the sake of sleeping better, don't take sedatives such as eszopiclone (Lunesta) zolpidem (Ambien) with a meal.

Mood stabilizers such as lithium and divalproex sodium (Depakote) should be taken on a full stomach (as it may upset the stomach)

[I'll repost this in a separate thread, with the link]