  We present an analysis of constraints on the companion mass for the Galactic
microquasar GRS 1915+105. Using the known inclination angle and stability of
the jet axis, we can rule out massive ($M_s \ga 3 M_{\sun}$) companions with
orbital axes not aligned with the jet axis. For an aligned orbital axis, we
constrain the ratio of the stellar radius to the binary semi-major axis to be
$R_s/a <0.342$, based on the lack of X-ray eclipses. We then show that these
constraints together with the X-ray luminosity, approximate black hole mass,
and observations of the X-ray absorbing column density towards GRS 1915+105
rule out accretion via stellar wind from a massive companion, implying that
accretion occurs via Roche-lobe overflow. In that case, the constraint on
$R_s/a$ rules out any companion with $M_s > 19.4 M_{\sun}$ for a black hole
mass of $M_{BH} \simeq 30 M_{\sun}$. The lack of significant X-ray reprocessing
in the infrared from GRS 1915+105 also provides constraints on the mass and
temperature range of a Roche-lobe-filling mass donor.
