Tiny machine learning (TinyML) is a rapidly growing field aiming to democratize machine learning (ML) for resource-constrained microcontrollers (MCUs). Given the pervasiveness of these tiny devices, it is inherent to ask whether TinyML applications can benefit from aggregating their knowledge. Federated learning (FL) enables decentralized agents to jointly learn a global model without sharing sensitive local data. However, a common global model may not work for all devices due to the complexity of the actual deployment environment and the heterogeneity of the data available on each device. In addition, the deployment of TinyML hardware has significant computational and communication constraints, which traditional ML fails to address. Considering these challenges, we propose TinyReptile, a simple but efficient algorithm inspired by meta-learning and online learning, to collaboratively learn a solid initialization for a neural network (NN) across tiny devices that can be quickly adapted to a new device with respect to its data. We demonstrate TinyReptile on Raspberry Pi 4 and Cortex-M4 MCU with only 256-KB RAM. The evaluations on various TinyML use cases confirm a resource reduction and training time saving by at least two factors compared with baseline algorithms with comparable performance.