Well it will depend on if you are talking the phone's text messages or if they are through a different app.
If through the phone's texting messaging app, then try these...
Option A
- Go to "Settings" and then tap "Accessibility".
- In here uncheck "Talk Back".
Option B
- Go to "Settings".
- In here tap "Voice Input" and then tap "Next".
- Now tap "Text-to-Speech".
- In here you should see "Driving Mode", turn it off.