Human anxiety is a grave mental health concern that needs to be addressed in the appropriate manner in order to develop a healthy society. In this study, an objective human anxiety assessment framework is developed by using physiological signals of electroencephalography (EEG) and recorded in response to exposure therapy. The EEG signals of twenty-three subjects from an existing database called "A Database for Anxious States which is based on a Psychological Stimulation (DASPS)" are used for anxiety quantification into two and four levels. The EEG signals are pre-processed using appropriate noise filtering techniques to remove unwanted ocular and muscular artifacts. Channel selection is performed to select the significantly different electrodes using statistical analysis techniques for binary and four-level classification of human anxiety, respectively. Features are extracted from the data of selected EEG channels in the frequency domain. Frequency band selection is applied to select the appropriate combination of EEG frequency bands, which in this study are theta and beta bands. Feature selection is applied to the features of the selected EEG frequency bands. Finally, the selected subset of features from the appropriate frequency bands of the statistically significant EEG channels were classified using multiple machine learning algorithms. An accuracy of 94.90% and 92.74% is attained for two and four-level anxiety classification using a random forest classifier with 9 and 10 features, respectively. The proposed state anxiety classification framework outperforms the existing anxiety detection framework in terms of accuracy with a smaller number of features which reduces the computational complexity of the algorithm.