Everyone will starve to death?

Not quite that level of an apocalypse.

It'd kill off, say, a few billion people. Places such as Mexico could still farm food, enough to sustain hundreds of thousands of people.
And the situation would recover fairly quickly - we'd almost certainly see a complete crash of global economy, energy prices soaring like never before and cannibalism becoming a viable survival strategy, but the end of the human rice? Hardly.