Usually you would need either an iPhone backup or an iTunes backup file like you mentioned.
There are third-party apps that claim to be able to recover iPhone messages, but they aren't free - and i have to say aren't guaranteed to work 100% of the time, so there is a little bit of risk involved.
If the message is important, then it might be worth searching for apps like Wondershare or Textsaver.
I would also recommend checking out this video, as they explain three different methods for recovering iPhone messages:
