Two-dimensional (2D) semiconductors are promising candidates for optoelectronic application and quantum information processes due to their inherent out-of-plane 2D confinement. In addition, they offer the possibility of achieving low-dimensional in-plane exciton confinement, similar to zero-dimensional quantum dots, with intriguing optical and electronic properties via strain or composition engineering. However, realizing such laterally confined 2D monolayers and systematically controlling size-dependent optical properties remain significant challenges. Here, we report the observation of lateral confinement of excitons in epitaxially grown in-plane MoSe2 quantum dots (~15-60 nm wide) inside a continuous matrix of WSe2 monolayer film via a sequential epitaxial growth process. Various optical spectroscopy techniques reveal the size-dependent exciton confinement in the MoSe2 monolayer quantum dots with exciton blue shift (12-40 meV) at a low temperature as compared to continuous monolayer MoSe2. Finally, single-photon emission was also observed from the smallest dots at 1.6 K. Our study opens the door to compositionally engineered, tunable, in-plane quantum light sources in 2D semiconductors.