Based on what I know there is no mantra meditation in Theravada vehicle. Although, in meditation, there is a technique like chanting Buddho, Buddho, etc., that is not a mantra that we are talking about.
In Hinduism, Mahayana, and Vajrayana, you can find it.
Every mantra in sanskrit has a meaning symbolically. In Mahayana, there are 10 level of bodhisatta. Each level of boddhisatva, for example level 7, already free from rebirth and have exceptional ability to see past life to certain amount, he still cannot make a mantra. Only bodhisattva level 8 up to Buddha can make mantra. This information can be found in Kalu Rinpoche book.
The way the mantra work is related to our subtle energy in our chakra, kundalini, etc.
In Theravada, so far I never find this information. Please correct me if I am wrong.
The big question is Did Buddha teach mantra meditation?
If we believe that all Buddha teaching are only in Pali text, the answer probably is no.
But, if we believe that Buddha teaching is so wide and appear in Pali, Sankrit, or other languages, the answer is yes.
I am not here nor there.
I am not right nor wrong.
I do not exist neither non-exist.
I am not I nor non-I.
I am not in samsara nor nirvana.
To All Buddhas, I bow down for the teaching of emptiness. Thank You!