An effective field theory framework is developed to study the interaction of heavy quarks in strongly coupled quark-gluon plasma (QGP). The latter is treated as a relativistic non-dissipative colorless fluid which can be studied using a derivatively coupled effective field theory based on previous work. Coupling this to heavy quarks provides systematic way to obtain the interaction between the heavy quark and phonons, excitations of the fluid. In particular we calculate the decay width of heavy quark to phonon and phonon-heavy quark scattering in a thermal medium.