Object recognition in unseen indoor environments remains a challenging problem for visual perception of mobile robots. In this letter, we propose the use of topologically persistent features, which rely on the objects' shape information, to address this challenge. In particular, we extract two kinds of features, namely, sparse persistence image (PI) and amplitude, by applying persistent homology to multi-directional height function-based filtrations of the cubical complexes representing the object segmentation maps. The features are then used to train a fully connected network for recognition. For performance evaluation, in addition to a widely used shape dataset and a benchmark indoor scenes dataset, we collect a new dataset, comprising scene images from two different environments, namely, a living room and a mock warehouse. The scenes are captured using varying camera poses under different illumination conditions and include up to five different objects from a given set of fourteen objects. On the benchmark indoor scenes dataset, sparse PI features show better recognition performance in unseen environments than the features learned using the widely used ResNetV2-56 and EfficientNet-B4 models. Further, they provide slightly higher recall and accuracy values than Faster R-CNN, an end-to-end object detection method, and its state-of-the-art variant, Domain Adaptive Faster R-CNN. The performance of our methods also remains relatively unchanged from the training environment (living room) to the unseen environment (mock warehouse) in the new dataset. In contrast, the performance of the object detection methods drops substantially. We also implement the proposed method on a real-world robot to demonstrate its usefulness.