The increased adoption of Internet of Things (IoT) devices has led to the generation of large data streams with applications in healthcare, sustainability, and robotics. In some cases, deep neural networks have been deployed directly on these resource-constrained units to limit communication overhead, increase efficiency and privacy, and enable real-time applications. However, a common challenge in this setting is the continuous adaptation of models necessary to accommodate changing environments, i.e., data distribution shifts. Test-time adaptation (TTA) has emerged as one potential solution, but its validity has yet to be explored in resource-constrained hardware settings, such as those involving microcontroller units (MCUs). TTA on constrained devices generally suffers from i) memory overhead due to the full backpropagation of a large pre-trained network, ii) lack of support for normalization layers on MCUs, and iii) either memory exhaustion with large batch sizes required for updating or poor performance with small batch sizes. In this paper, we propose TinyTTA, to enable, for the first time, efficient TTA on constrained devices with limited memory. To address the limited memory constraints, we introduce a novel self-ensemble and batch-agnostic early-exit strategy for TTA, which enables continuous adaptation with small batch sizes for reduced memory usage, handles distribution shifts, and improves latency efficiency. Moreover, we develop the TinyTTA Engine, a first-of-its-kind MCU library that enables on-device TTA. We validate TinyTTA on a Raspberry Pi Zero 2W and an STM32H747 MCU. Experimental results demonstrate that TinyTTA improves TTA accuracy by up to 57.6\%, reduces memory usage by up to six times, and achieves faster and more energy-efficient TTA. Notably, TinyTTA is the only framework able to run TTA on MCU STM32H747 with a 512 KB memory constraint while maintaining high performance.