We consider the effect of a time-varying Planck mass on the propagation of gravitational waves (GWs). A running Planck mass arises naturally in several modified-gravity theories, and here we focus on those that carry an additional dark energy field responsible for the late-time accelerated expansion of the Universe, yet—like general relativity (GR)—propagate only two GW polarizations, both traveling at the speed of light. Because a time-varying Planck mass affects the amplitude of the GWs and therefore the inferred distance to the source, standard siren measurements of H0 are degenerate with the parameter cM characterizing the time-varying Planck mass, where cM=0 corresponds to GR with a constant Planck mass. The effect of nonzero cM will have a noticeable impact on GWs emitted by binary neutron stars (BNSs) at the sensitivities and distances observable by ground-based GW detectors such as Advanced LIGO and A + , implying that standard siren measurements can provide joint constraints on H0 and cM. Assuming a Λ cold dark matter evolution of the Universe and taking Planck's measurement of H0 as a prior, we find that GW170817 constrains cM=-9-28+21 (68.3% credibility). We also discuss forecasts, finding that if we assume H0 is known independently (e.g., from the cosmic microwave background), then 100 BNS events detected by Advanced LIGO can constrain cM to within ±0.9 . This is comparable to the current best constraints from cosmology. Similarly, for 100 LIGO A + BNS detections, it is possible to constrain cM to ±0.5 . When analyzing joint H0 and cM constraints we find that ̃400 LIGO A + events are needed to constrain H0 to 1% accuracy. Finally, we discuss the possibility of a nonzero value of cM biasing standard siren H0 measurements from 100 LIGO A + detections, and find that cM=+1.35 could bias H0 by 3 σ to 4 σ too low if we incorrectly assume cM=0 .