Recent gravitational wave observations have allowed stringent new constraints on modifications to General Relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans-Dicke-Fierz theory as an example. Using the stationary phase approximation and the post-circular approximation (an expansion in small eccentricity), we first construct an analytical expression for frequency-domain gravitational waveforms produced by inspiraling compact binaries with small eccentricity in this theory. We then calculate the overlap between our approximate analytical waveforms and an eccentric numerical model (TaylorT4) to determine the regime of validity (in eccentricity) of the former. With this at hand, we carry out a Fisher analysis to determine the accuracy to which Jordan-Brans-Dicke-Fierz theory could be constrained given future eccentric detections consistent with General Relativity. We find that the constraint on the theory initially deteriorates (due to covariances between the eccentricity and the Brans-Dicke coupling parameter), but then it begins to recover, once the eccentricity is larger than approximately 0.03. We also find that third-generation ground-based detectors and space-based detectors could allow for constraints that are up to an order of magnitude more stringent than current Solar System bounds. Our results suggest that waveforms in modified gravity for systems with moderate eccentricity should be developed to maximize the theoretical physics that can be extracted in the future. * sma@caltech.edu † nyunes@illinois.edu binaries in galactic nuclei, which can lead to orbits with eccentricities around 0.05-0.2 when the low harmonics of the GW enter the LISA band [18].Even if eccentric binaries are not detectable in the current observing runs of advanced LIGO and Virgo, eccentric binaries will be detected by both second-and thirdgeneration detectors once they reach their design sensitivity, as argued by multiple authors (see e.g.[19] and references therein). Reference [19] found that advanced LIGO-type detectors could detect approximately 0.1-10 events per year out to redshifts z ∼ 0.2, while an array of Einstein Telescope (ET) detectors could detect hundreds of events per year to redshift z ∼ 2.3. According to [20], advanced LIGO (aLIGO) will be upgraded to A+ by 2022 and to Voyager by 2027, although these dates are likely to slip somewhat. Third-generation detectors, like ET and Cosmic Explorer (CE), are also planned in the 2030s. The space-based gravitational wave detector, LISA, is expected to be launched in the mid 2030s [21]. Given these plans for improved GW detectors, the accurate and efficient inclusion of eccentricity in GW models is both interesting and timely.One could in princ...