Prophecy and prophesy are closely related, but they do not do the same job in a sentence.
Prophecy is a noun. It means a prediction or an inspired message about the future. You use it when you are naming the message itself. Example: The prophecy warned of a great storm.
Prophesy is a verb. It means to speak, reveal, or write a prophecy. You use it when someone is doing the action. Example: The priest claimed he could prophesy coming events.
A simple way to keep them straight is this: prophecy names the thing, while prophesy names the act.
- Correct: Her prophecy surprised the crowd.
- Correct: Some people believed she could prophesy disaster.
- Incorrect: Her prophesy surprised the crowd. This should be prophecy because it names the message.
If you can replace the word with prediction, choose prophecy. If you mean to predict in a spiritual or inspired sense, choose prophesy.