Objective: This study aimed to determine the correlation between the incidence of acute mountain sickness (AMS) and the body constitution of Tibetan medicine and other relevant factors to provide a reference for the prediction and prevention of AMS. Methods: A case–control study was conducted to recruit participants who experienced or did not experience AMS after entering a plateau. The data was collected through online questionnaires for convenient sampling. Demographic characteristics, body constitution, and related states or behaviors were investigated before and after entering the plateau. The participants were divided into case and control groups based on the incidence of AMS. The distributions of relevant factors were compared. Binary logistic regression analysis was used to screen for risk and protective factors. Results: There were 167 participants who completed the questionnaire. A total of 54 cases were excluded, and 113 participants were included, including 52 in the case group and 61 in the control group. In the case group, 37, 13, and 2 patients had mild, moderate, and severe AMS, respectively. In terms of the Tibetan medicine constitution, the case group had the highest proportion of Bad-rlung (25.0%) and Rlung types (21.2%), whereas the control group had the highest proportion of Bad-rlung (29.5%) and Mkhris-bad types (24.6%). There was no significant difference in the distribution of the constitutional types between the two groups. Insomnia or insufficient sleep within the week prior to entering the plateau and fatigue after arrival were risk factors for AMS, with odds ratios (OR) and 95% confidence intervals (CI) of 5.012 (1.871–13.426) and 3.387 (1.393–8.236), respectively. A history of short-term plateau travel is a protective factor for AMS (OR: 0.32, 95% CI: 0.129 to 0.792). Conclusion Insomnia or lack of sleep before ascending to a plateau and fatigue after arrival are risk factors for AMS. The Rlung constitution might be related to the incidence of AMS; however, this still needs to be verified in large-sample observational studies. The risk factors identified in this study can provide a reference for the prevention practice and research of AMS.