Double electron capture is a rare nuclear decay process in which two orbital electrons are captured simultaneously in the same nucleus. Measurement of its two-neutrino mode would provide a new reference for the calculation of nuclear matrix elements whereas observation of its neutrinoless mode would demonstrate lepton number violation. A search for two-neutrino double electron capture on <sup>124sup>Xe is performed using 165.9 days of data collected with the XMASS-I liquid xenon detector. No significant excess above background was observed and we set a lower limit on the half-life as <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301861&_mathId=si1.gif&_user=111111111&_pii=S0370269316301861&_rdoc=1&_issn=03702693&md5=fc6e63657d5313cf205ec921a9729ace" title="Click to view the MathML source">4.7×10<sup>21sup>span><span class="mathContainer hidden"><span class="mathCode"><math altimg="si1.gif" overflow="scroll"><mn>4.7mn><mo>×mo><msup><mrow><mn>10mn>mrow><mrow><mn>21mn>mrow>msup>math>span>span>span> years at 90% confidence level. The obtained limit has ruled out parts of some theoretical expectations. We obtain a lower limit on the <sup>126sup>Xe two-neutrino double electron capture half-life of <span id="mmlsi2" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301861&_mathId=si2.gif&_user=111111111&_pii=S0370269316301861&_rdoc=1&_issn=03702693&md5=a75d4b60192dc9a8ce7d05780a325819" title="Click to view the MathML source">4.3×10<sup>21sup>span><span class="mathContainer hidden"><span class="mathCode"><math altimg="si2.gif" overflow="scroll"><mn>4.3mn><mo>×mo><msup><mrow><mn>10mn>mrow><mrow><mn>21mn>mrow>msup>math>span>span>span> years at 90% confidence level as well.