State-of-the-art text classification models are becoming increasingly reliant on deep neural networks (DNNs). Due to their black-box nature, faithful and robust explanation methods need to accompany classifiers for deployment in real-life scenarios. However, it has been shown that explanation methods in vision applications are susceptible to local, imperceptible perturbations that can significantly alter the explanations without changing the predicted classes. We show here that the existence of such perturbations extends to text classifiers as well. Specifically, we introduce TextExplanationFooler (TEF), a novel explanation attack algorithm that alters text input samples imperceptibly so that the outcome of widely-used explanation methods changes considerably while leaving classifier predictions unchanged. We evaluate the attribution robustness estimation performance of TEF on five text classification datasets, utilizing three DNN architectures and a transformer architecture for each dataset. By significantly decreasing the correlation between unchanged and perturbed input attributions, we show that all models and explanation methods are susceptible to TEF perturbations. Moreover, we evaluate how the perturbations transfer to other model architectures and attribution methods, finding better than random performance in scenarios where the exact attacked model and explanation method are unknown. Finally, we introduce a semi-universal attack that is able to compute fast, computationally light perturbations with no knowledge of the attacked classifier nor explanation method. Overall, our work shows that explanations in text classifiers are fragile and users need to carefully address their robustness before relying on them in critical applications.