This study explores the application of quantum machine learning (QML) algorithms to enhance cybersecurity threat detection, particularly in the classification of malware and intrusion detection within high-dimensional datasets. Classical machine learning approaches encounter limitations when dealing with intricate, obfuscated malware patterns and extensive network intrusion data. To address these challenges, we implement and evaluate various QML algorithms, including Quantum Neural Networks (QNN), Quantum Support Vector Machines (QSVM), and hybrid Quantum Convolutional Neural Networks (QCNN) for malware detection tasks. Our experimental analysis utilized two datasets: the Intrusion dataset, comprising 150 samples with 56 memory-based features derived from Volatility framework analysis, and the ObfuscatedMalMem2022 dataset, containing 58,596 samples with 57 features representing benign and malicious software. Remarkably, our QML methods demonstrated superior performance compared to classical approaches, achieving accuracies of 95% for QNN and 94% for QSVM. These quantum-enhanced methods leveraged quantum superposition and entanglement principles to accurately identify complex patterns within highly obfuscated malware samples that were imperceptible to classical methods. To further advance malware analysis, we propose a novel real-time malware analysis framework that incorporates Quantum Feature Extraction using Quantum Fourier Transform, Quantum Feature Maps, and Classification using Variational Quantum Circuits. This system integrates explainable AI methods, including GradCAM++ and ScoreCAM algorithms, to provide interpretable insights into the quantum decision-making processes.