Accurate prediction of SARS-CoV-2 infection based on symptoms can be a cost-efficient tool for remote screening in healthcare settings with limited SARS-CoV-2 testing capacity. We used a machine learning approach to determine self-reported symptoms that best predict a positive SARS-CoV-2 test result in physician trainees from a large healthcare system in New York. We used survey data on symptoms history and SARS-CoV-2 testing results collected retrospectively from 328 physician trainees in the Mount Sinai Health System, over the period 1 February 2020 to 31 July 2020. Prospective data on symptoms reported prior to SARS-CoV-2 test results were available from the employee health service COVID-19 registry for 186 trainees and analyzed to confirm absence of recall bias. We estimated the associations between symptoms and IgG antibody and/or reverse transcriptase polymerase chain reaction test results using Bayesian generalized linear mixed effect regression models adjusted for confounders. We identified symptoms predicting a positive SARS-CoV-2 test result using extreme gradient boosting (XGBoost). Cough, chills, fever, fatigue, myalgia, headache, shortness of breath, diarrhea, nausea/vomiting, loss of smell, loss of taste, malaise and runny nose were associated with a positive SARS-CoV-2 test result. Loss of taste, myalgia, loss of smell, cough and fever were identified as key predictors for a positive SARS-CoV-2 test result in the XGBoost model. Inclusion of sociodemographic and occupational risk factors in the model improved prediction only slightly (from AUC = 0.822 to AUC = 0.838). Loss of taste, myalgia, loss of smell, cough and fever are key predictors for symptom-based screening of SARS-CoV-2 infection in healthcare settings with remote screening and/or limited testing capacity.