IoT devices and networks are distributed by nature and very often IoT devices are deployed at remote locations with limited physical access. To ensure the latest firmware, security patches & configuration settings in remote IoT devices, Original Equipment Manufacturers (OEMs) send device-specific, Over-The-Air (OTA) packages in a scalable way. The OTA updates are a great facility to update and control distributed IoT devices remotely using cloud services. However, so far, the major focus of OTA is generally limited to remote patching or updates to remove any software bugs and security flaws. Recently, Edge Computing is getting popular where IoT devices are equipped with ML data models to perform edge analytics at the device level. However, existing methods to deploy ML models on IoT devices still require physical access to the devices. OTA techniques for ML models deployments bring unique challenges such as security & privacy issues due to remote access, limited resources at the device level to fit in ML models, and diverse hardware and software specifications of IoT devices. This paper presents a novel OTA technique to remotely deploy tiny ML models over IoT devices and perform tasks such as ML model updates, firmware re-flashing, re-configuration, or re-purposing. We discuss relevant challenges for OTA ML deployment over IoT both at the scientific and engineering level. We propose an IoT hardware-friendly approach named OTATinyML to enable resource-constrained IoT devices to perform end-to-end fetching, storage, and execution of many TinyML models. OTA-TinyML loads the C source file of ML models from a web server into the embedded IoT devices via HTTPS. It is compatible with a range of IoT development boards and ML models from text, speech & image domains. OTA-TinyML is tested by performing remote fetching of 6 types of ML models, storing them on 4 types of memory units, then loading and executing on 7 popular MCU boards.