Leaf area index (LAI) and leaf dry matter (LDM) are important indices of crop growth. Real-time, nondestructive monitoring of crop growth is instructive for the diagnosis of crop growth and prediction of grain yield. Unmanned aerial vehicle (UAV)-based remote sensing is widely used in precision agriculture due to its unique advantages in flexibility and resolution. This study was carried out on wheat trials treated with different nitrogen levels and seeding densities in three regions of Jiangsu Province in 2018–2019. Canopy spectral images were collected by the UAV equipped with a multi-spectral camera during key wheat growth stages. To verify the results of the UAV images, the LAI, LDM, and yield data were obtained by destructive sampling. We extracted the wheat canopy reflectance and selected the best vegetation index for monitoring growth and predicting yield. Simple linear regression (LR), multiple linear regression (MLR), stepwise multiple linear regression (SMLR), partial least squares regression (PLSR), artificial neural network (ANN), and random forest (RF) modeling methods were used to construct a model for wheat yield estimation. The results show that the multi-spectral camera mounted on the multi-rotor UAV has a broad application prospect in crop growth index monitoring and yield estimation. The vegetation index combined with the red edge band and the near-infrared band was significantly correlated with LAI and LDM. Machine learning methods (i.e., PLSR, ANN, and RF) performed better for predicting wheat yield. The RF model constructed by normalized difference vegetation index (NDVI) at the jointing stage, heading stage, flowering stage, and filling stage was the optimal wheat yield estimation model in this study, with an R² of 0.78 and relative root mean square error (RRMSE) of 0.1030. The results provide a theoretical basis for monitoring crop growth with a multi-rotor UAV platform and explore a technical method for improving the precision of yield estimation.