We propose a Mach-Zehnder electro-optic modulator (MZM) in which conventional waveguide Y branches are replaced by a tunable 2 × 2 coupler and a 1 × 2 coupler based on multimode interference (MMI). The properties of the MMI couplers, which were designed with tapered input/output waveguides, were experimentally evaluated. The MZM was fabricated with Ti-diffused LiNbO$_{3}$ waveguides. Optical intensity modulation was achieved with a 50 dB extinction ratio. The experimental results show that the 2 × 2 MMI optical coupler provides nearly equal power division with a 90$^\circ$ phase difference, which means that the coupler operates as an optical 90$^\circ$ hybrid. This MZM structure was applied to optical single-sideband modulation. A high sideband suppression ratio of 39 dB was achieved in a modulation experiment with microwave modulation signals. We also designed and fabricated a compact optical single-sideband modulator, in which the microwave 90$^\circ$ hybrid circuit was integrated on a LiNbO$_{3}$ substrate, that operates with a single input signal. This modulator was confirmed to have a consistently high sideband suppression ratio, which was achieved by tuning the optical power splitting ratio of the 2 × 2 MMI coupler to compensate for the effects of fabrication errors and deviations in the operating conditions.