We examine the possibility of using single-Higgs production at an e+e− collider with polarized beams to measure, or constrain, indirectly a possible anomalous triple-Higgs coupling, which can contribute to the process via one-loop diagrams. In the dominant process e+e−→ZH, longitudinally polarized beams can lead to an improvement in the cross-section by 50% for e− and e+ polarizations of −0.8 and +0.3, respectively. This corresponds to an improvement in the sensitivity to the triple-Higgs coupling of about 18% for a center-of-mass energy of 250 GeV and an integrated luminosity of 2 ab−1, making a strong case of beam polarization. This also implies that with polarized beams, the luminosity needed to get a particular sensitivity is less by about 33% as compared to that needed with unpolarized beams. Even when only the e− beam is polarized −0.8, the improvement in the sensitivity is about 8%. We also study the effect of longitudinal beam polarization on the sensitivity to the triple-Higgs coupling of Higgs production through the subdominant process e+e−→Hνˉν occurring through WW fusion.