The effects of quantum confinement on excitons in parabolic quantum dots of monolayer transition metal dichalcogenides (TMDC QDs) are investigated within a massive Dirac fermion model. A giant spin-valley coupling of the TMDC QDs is obtained, larger than that of monolayer TMDC sheets and consistent with recent experimental measurements. The exciton transition energy and the binding energy are calculated, and it is found that the strong quantum confinement results in extremely high exciton binding energies. The enormously large exciton binding energy in TMDC QDs ((EB2D 500 meV) < EBQD 1800 meV for different kinds of TMDC QDs) ensures that the many body interactions play a significant role in the investigation of the optical properties of these novel nanostructures. The estimated oscillator strength and radiative lifetime of excitons are strongly size-dependent and indicate a giant oscillator strength enhancement and ultrafast radiative annihilation of excitons, varying from a few tens of femtoseconds to a few picoseconds. We found that the spin-dependent band gap, spin-valley coupling, binding energy and excitonic effects can be tuned by quantum confinements, leading to tunable quantum dots in monolayer TMDCs. This finding offers new functionality in engineering the interaction of a 2D material with light and creates promise for the quantum manipulation of spin and valley degrees of freedom in TMDC nanostructures, enabling versatile novel 2D quantum photonic and optoelectronic nanodevices.