Deep Neural Network (DNN) classifiers are known to be vulnerable to Trojan or backdoor attacks, where the classifier is manipulated such that it misclassifies any input containing an attacker-determined Trojan trigger. Backdoors compromise a model's integrity, thereby posing a severe threat to the landscape of DNN-based classification. While multiple defenses against such attacks exist for classifiers in the image domain, there have been limited efforts to protect classifiers in the text domain. We present Trojan-Miner (T-Miner) -- a defense framework for Trojan attacks on DNN-based text classifiers. T-Miner employs a sequence-to-sequence (seq-2-seq) generative model that probes the suspicious classifier and learns to produce text sequences that are likely to contain the Trojan trigger. T-Miner then analyzes the text produced by the generative model to determine if they contain trigger phrases, and correspondingly, whether the tested classifier has a backdoor. T-Miner requires no access to the training dataset or clean inputs of the suspicious classifier, and instead uses synthetically crafted "nonsensical" text inputs to train the generative model. We extensively evaluate T-Miner on 1100 model instances spanning 3 ubiquitous DNN model architectures, 5 different classification tasks, and a variety of trigger phrases. We show that T-Miner detects Trojan and clean models with a 98.75% overall accuracy, while achieving low false positives on clean models. We also show that T-Miner is robust against a variety of targeted, advanced attacks from an adaptive attacker.