Single-mode high-index-contrast waveguides have been ubiquitously exploited in optical, microwave, and phononic structures for achieving enhanced wave-matter interactions. Although micro-scale optomechanical and electro-optical devices have been widely studied, optomagnonic devices remain a grand challenge at the microscale. Here, we introduce a planar optomagnonic waveguide platform based on a ferrimagnetic insulator that simultaneously supports single transverse mode of spin waves (magnons) and highly confined optical modes. The co-localization of spin and light waves gives rise to enhanced inverse Faraday effect, and as a result, magnons are excited by an effective magnetic field generated by interacting optical photons. Moreover, the strongly enhanced optomagnonic interaction allows us to observe such effect using low-power (milliwatt level) light signals in the continuous-wave form, as opposed to high-intensity (megawatt peak power) light pulses that are typically required in magnetic bulk materials or thin films. The optically-driven magnons are detected electrically with preserved phase coherence, showing the feasibility for launching spin waves with low-power continuous optical fields.