Traditional diagnostic methods for asthma, a widespread chronic respiratory illness, are often limited by factors such as patient cooperation with spirometry. Non-invasive acoustic analysis using machine learning offers a promising alternative for objective diagnosis by analyzing vocal characteristics. This study aimed to develop and validate a robust classification model for adult asthma using acoustic features from the vocalized /ɑː/ sound. In a case-control study, voice recordings of the /ɑː/ sound were collected from a primary cohort of 214 adults and an independent external validation cohort of 200 adults. This study extracted features using a modified extended Geneva Minimalistic Acoustic Parameter Set and compared seven machine learning models. The top-performing model, Extreme Gradient Boosting, was further assessed through ten-fold cross-validation, external validation, and feature analysis using SHapley Additive exPlanations and Local Interpretable Model-Agnostic Explanations. The Extreme Gradient Boosting classifier achieved the highest performance on the test set, with an accuracy of 0.8514, an Area Under the Curve of 0.9130, a recall of 0.8804, a precision of 0.8387, an F1-score of 0.8567, a Kappa coefficient of 0.7018, and a Matthews Correlation Coefficient of 0.7071. On the external validation set, the model maintained strong performance with an accuracy of 0.8100, AUC of 0.8755, recall of 0.8300, precision of 0.7981, F1-score of 0.8137, Kappa of 0.6200, and Matthews Correlation Coefficient of 0.6205. Interpretability analysis identified formant frequencies as the most significant acoustic predictors. An Extreme Gradient Boosting model utilizing features from the extended Geneva Minimalistic Acoustic Parameter Set is an accurate and viable non-invasive method for classifying adult asthma, holding significant potential for developing accessible tools for early diagnosis, remote monitoring, and improved asthma management.