High-resolution sea surface temperature (SST) estimates are dependent on satellite-based infrared radiometers, which are proven to be highly accurate in the past decades. However, the presence of clouds is a big stumbling block when physical approaches are used to derive SST. This problem is more prominent across tropical regions such as Arabian Sea(AS) and Bay of Bengal(BoB), restricting the availability of high-resolution SST data for ocean applications. The previous studies for developing daily high-resolution cloud-free SST products mainly focus on fusion of multiple satellites and in-situ data products that are computationally expensive and often time consuming. At the same time, it was observed that the capabilities of data-driven approaches are not yet fully explored in the estimation of cloud-free high-resolution SST data. Hence, in this study an attempt has been made for the first time to estimate daily cloud free SST from a single sensor (MODIS Aqua) dataset using advanced machine learning techniques. Here, three distinct machine learning techniques such as Artificial Neural Networks (ANN), Support Vector Regression (SVR) and Random Forest (RF)-based algorithms were developed and evaluated over two different study areas within the AS and BoB using 10 years of MODIS data and in-situ reference data. Among the developed algorithms, the SVR-based algorithm performs consistently better. In AS region, while testing, the SVR-based SST estimates was able to achieve an adjusted coefficient of determination (R_adj^2) of 0.82 and root mean square error (RMSE) of 0.71°C with respect to the in situ data. Similarly, in BoB too, the SVR algorithm outperforms the other algorithms with R_adj^2 of 0.78 with RMSE of 0.88ºC. Further, a spatio-temporal and visual analysis of the results as well as an inter-comparision with NOAA AVHRR daily optimally interpolated global SST (a standard SST product available in practice) the suggest that the proposed SVR-based algorithm has huge potential to produce operational high-resolution cloud-free SST estimates, even if there is cloud cover in the image.