Detecting and characterizing oil spills in arctic environments is challenging due to the presence of sea ice. Methods based on Ground-Penetrating Radars and acoustic sensors were used in the literature to detect oil in ice-covered waters; however, their implementation is costly, and their capabilities are limited in terms of oil-thickness estimation. To address this problem, we propose a new low-cost sensing system based on a planar capacitive sensor that can detect the presence of oil under ice sheets and measure its thickness and depth. Our proposed sensor is based on movable dual electrodes mounted next to each other on the same sensing plane. The electric field created between the electrodes extends beneath the sensing plane and is affected by the electric properties of the sensed material (ice, oil, or water). Changes in the mutual capacitance of the electrodes are related to changes in the thickness and depth of the embedded oil phase. The capacitance of the sensor is measured at two different excitation frequencies while changing the horizontal separation distance between the electrodes. These measurements are collected to create a dataset for training machine-learning-based classification and regression models to detect the presence of oil and measure its thickness and depth. In comparison with the available sensing techniques, our proposed sensor has several advantages, such as being noninvasive or non-intrusive, simple to manufacture, safe to operate, and having low cost and low maintenance requirements. The experimental evaluation described in this paper demonstrates the effectiveness of our proposed system, which showed a very high detection accuracy of more than 90% and an accurate thickness and depth estimation capability with a Mean Absolute Error (MAE) of around 0.5 cm for thickness and depth estimations for oil thicknesses ranging between 0.5 cm and 8 cm and for oil depths ranging between 2 and 5 cm.