In this work, we address the novel and challenging problem of domain adaptive 3D shape retrieval from single 2D images (DA-IBSR). While the existing image-based 3D shape retrieval (IBSR) problem focuses on modality alignment for retrieving a matchable 3D shape from a shape repository given a 2D image query, it does not consider any distribution shift between the training and testing image-shape pairs, making the performance of off-the-shelves IBSR methods subpar. In contrast, the proposed DA-IBSR addresses the non-trivial problem of modality shift as well distribution shift across training and test sets. To address these issues, we propose an end-to-end trainable model called DAIS-NET. Our objective is to align the images and shapes separately from both domains while simultaneously learn a shared embedding space for the 2D and 3D modalities. The former problem is addressed by separately employing maximum mean discrepancy loss across the 2D images and 3D shapes of the two domains. To address the modality alignment, we incorporate the notion of negative sample mining and employ triplet loss to bridge the gap between positive 2D-3D pairs (of same class) and increase the separation between negative 2D-3D pairs (of different class). Additionally, we employ an entropy minimization strategy to align the unlabeled target domain data in the semantic space. To evaluate our proposed approach, we define the experimental setting of DA-IBSR on the following benchmarks: SHREC'14 <-> Pix3D and ShapeNet <-> SHREC'14. Considering the novelty of the problem statement, we have demonstrated that the issue of domain gap is prevalent by comparing our method with the existing literature. Additionally, through extensive evaluations, we demonstrate the capability of DAIS-NET to successfully mitigate this domain gap in image based 3D shape retrieval.