The information on biophysical parameters—such as height, crown area, and vegetation indices such as the normalized difference vegetation index (NDVI) and normalized difference red edge index (NDRE)—are useful to monitor health conditions and the growth of oil palm trees in precision agriculture practices. The use of multispectral sensors mounted on unmanned aerial vehicles (UAV) provides high spatio-temporal resolution data to study plant health. However, the influence of UAV altitude when extracting biophysical parameters of oil palm from a multispectral sensor has not yet been well explored. Therefore, this study utilized the MicaSense RedEdge sensor mounted on a DJI Phantom–4 UAV platform for aerial photogrammetry. Three different close-range multispectral aerial images were acquired at a flight altitude of 20 m, 60 m, and 80 m above ground level (AGL) over the young oil palm plantation area in Malaysia. The images were processed using the structure from motion (SfM) technique in Pix4DMapper software and produced multispectral orthomosaic aerial images, digital surface model (DSM), and point clouds. Meanwhile, canopy height models (CHM) were generated by subtracting DSM and digital elevation models (DEM). Oil palm tree heights and crown projected area (CPA) were extracted from CHM and the orthomosaic. NDVI and NDRE were calculated using the red, red-edge, and near-infrared spectral bands of orthomosaic data. The accuracy of the extracted height and CPA were evaluated by assessing accuracy from a different altitude of UAV data with ground measured CPA and height. Correlations, root mean square deviation (RMSD), and central tendency were used to compare UAV extracted biophysical parameters with ground data. Based on our results, flying at an altitude of 60 m is the best and optimal flight altitude for estimating biophysical parameters followed by 80 m altitude. The 20 m UAV altitude showed a tendency of overestimation in biophysical parameters of young oil palm and is less consistent when extracting parameters among the others. The methodology and results are a step toward precision agriculture in the oil palm plantation area.