Motor imagery (MI) classification based on electroencephalogram (EEG) is a widely-used technique in non-invasive brain-computer interface (BCI) systems. Since EEG recordings suffer from heterogeneity across subjects and labeled data insufficiency, designing a classifier that performs the MI independently from the subject with limited labeled samples would be desirable. To overcome these limitations, we propose a novel subject-independent semi-supervised deep architecture (SSDA). The proposed SSDA consists of two parts: an unsupervised and a supervised element. The training set contains both labeled and unlabeled data samples from multiple subjects. First, the unsupervised part, known as the columnar spatiotemporal auto-encoder (CST-AE), extracts latent features from all the training samples by maximizing the similarity between the original and reconstructed data. A dimensional scaling approach is employed to reduce the dimensionality of the representations while preserving their discriminability. Second, a supervised part learns a classifier based on the labeled training samples using the latent features acquired in the unsupervised part. Moreover, we employ center loss in the supervised part to minimize the embedding space distance of each point in a class to its center. The model optimizes both parts of the network in an end-to-end fashion. The performance of the proposed SSDA is evaluated on test subjects who were not seen by the model during the training phase. To assess the performance, we use two benchmark EEG-based MI task datasets. The results demonstrate that SSDA outperforms state-of-the-art methods and that a small number of labeled training samples can be sufficient for strong classification performance.