Sufficient condition for simple module

Every non-zero module homomorphism $f:M\rightarrow N$ is injective. Prove that $M$ is simple.

$f$ is not the zero map so $M$ is not $\{0\}$. I'm guessing I should let $N$ be a proper submodule of $M$ and pick a non-zero module homomorphism for which $N$ is the kernel. Any ideas?

Thanks

Consider the projection $M \twoheadrightarrow M/N$.