In patients with obstructive coronary artery disease, the functional significance of a coronary artery stenosis needs to be determined to guide treatment. This is typically established through fractional flow reserve (FFR) measurement, performed during invasive coronary angiography (ICA). We present a method for automatic and non-invasive detection of patients requiring ICA, employing deep unsupervised analysis of complete coronary arteries in cardiac CT angiography (CCTA) images. We retrospectively collected CCTA scans of 187 patients, 137 of them underwent invasive FFR measurement in 192 different coronary arteries. These FFR measurements served as a reference standard for the functional significance of the coronary stenosis. The centerlines of the coronary arteries were extracted and used to reconstruct straightened multi-planar reformatted (MPR) volumes. To automatically identify arteries with functionally significant stenosis that require ICA, each MPR volume was encoded into a fixed number of encodings using two disjoint 3D and 1D convolutional autoencoders performing spatial and sequential encodings, respectively. Thereafter, these encodings were employed to classify arteries using a support vector machine classifier. The detection of coronary arteries requiring invasive evaluation, evaluated using repeated cross-validation experiments, resulted in an area under the receiver operating characteristic curve of $0.81 \pm 0.02$ on the artery-level, and $0.87 \pm 0.02$ on the patient-level. The results demonstrate the feasibility of automatic non-invasive detection of patients that require ICA and possibly subsequent coronary artery intervention. This could potentially reduce the number of patients that unnecessarily undergo ICA.