A light CP-even Standard Model (SM) gauge-singlet scalar $S$ can be produced abundantly in the supernova core, via the nucleon bremsstrahlung process $N N to N N S$, due to its mixing with the SM Higgs boson. Including the effective $S$ coupling to both nucleons and the pion mediators, we evaluate the production amplitude for the $S$ particle and point out a key difference with the well-known light CP-odd scalar (axion) and vector boson (dark photon) cases. Taking the subsequent decay and re-absorption of $S$ into account, we present a complete calculation of the energy loss rate for the $S$ particle. We then use the SN1987A luminosity constraints to derive updated supernova limits on the mixing of the scalar $S$ with the SM Higgs boson. We find that the mixing angle $sintheta$ with the SM Higgs is excluded only in the narrow range of $3.9 times 10^{-7}$ to $7.0 times 10^{-6}$, depending on the scalar mass up to about 147 MeV, beyond which the supernova limit disappears.
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