In this paper, the power control problem is addressed in a wireless interference network in which there exist multiple transmitter-receiver pairs sharing the same bandwidth for information exchange. The goal is to train a common deep neural network (DNN) for power allocation at each transmitter. Recent studies in the literature have addressed this problem via deep reinforcement learning (DRL). However, training DRL algorithms can become costly in wireless networks since the DRL algorithm may converge slowly in specific problems and hence require a large amount of training data. Besides, the converged model may fail in a new environment, which is not preferable in a wireless network due to its dynamic and time-varying nature. In this work, we address these considerations by proposing a meta-DRL framework that incorporates the method of Model-Agnostic Meta-Learning (MAML). Within the proposed framework, a common initialization is trained for similar power control tasks. From the initialization, we show that only a few gradient descent steps are required for adapting to an unseen task. Simulation results demonstrate that the proposed framework can outperform conventional DRL and joint-learning (which trains a global model for similar tasks) for power control in wireless interference networks.