Not necessarily. It's a trope that you might see in a TV drama. But I would bet that most of the time when somebody says this they simply mean "the moon's pretty" without any deeper meaning. For it to mean "I love you" there needs to be a few pre-conditions not least of which that you have to be with somebody you like romantically when you say it.
There's a well-known episode where a famous novelist 夏目漱石 Natsume Sōseki translated "I love you" like that in Meiji period. When he was a professor of Tokyo Imperial University, a student translated "I love you" to 私はあなたを愛しています(我汝を愛す in classical Japanese). Sōseki said "Japanese people usually don't say such words. Instead, we say, for example, 月が綺麗ですね with watching the moon together."
Incidentally, it's considered that this is a fake episode. There is no evidence to proof that he really said this translation.