Northeast China plays a pivotal role in producing commodity grains. The precipitation and temperature distribution during the growth season is impacted by geographical and climate factors, rendering the region vulnerable to drought. However, relying on a single index does not reflect the severity and extent of drought in different regions. This research utilised the random forest (RF) model for screening remote sensing indices. Relative soil moisture (RSM) was employed to compare seven commonly used indices: the temperature vegetation dryness index (TVDI), vegetation supply water index (VSWI), vegetation condition index (VCI), temperature condition index (TCI), vegetation health index (VHI), multi-band drought index (MBDI), and normalised difference drought index (NDDI). The effectiveness of these indices for monitoring drought during different developmental stages of spring maize was evaluated. Trend rates were employed to investigate the temporal changes in drought patterns of spring maize from 2003 to 2020, and the Sen + Mann–Kendall test was used to analyse spatial variations. The results showed the following: (1) The seven remote sensing indices could accurately track drought during critical growth stages with the TVDI demonstrating higher applicability than the other six indices. (2) The application periods of two TVDIs with different parameters differed for the drought monitoring of spring maize in different developmental periods. The consistency and accuracy of the normalised difference vegetation index (NDVI)-based TVDI (TVDIN) were 5.77% and 34.62% higher than those of the enhanced vegetation index (EVI)-based TVDI (TVDIE), respectively, in the early stage. In contrast, the TVDIE exhibited 13.46% higher consistency than the TVDIN in the middle stage, and the accuracy was the same. During the later stage, the TVDIE showed significantly higher consistency and accuracy than the TVDIN with consistency increases of 9.61% and 38.64%, respectively. (3) The drought trend in northeast China increased from 2003 to 2020, exhibiting severe spring drought and a weakening of the drought in summer. The southern, southwestern, and northwestern parts of northeast China showed an upward drought trend; the drought-affected areas accounted for 37.91% of the study area. This paper identified the most suitable remote sensing indices for monitoring drought in different developmental stages of spring maize. The results provide a comprehensive understanding of the spatial–temporal patterns of drought during the past 18 years. These findings can be used to develop a dynamic agricultural drought monitoring model to ensure food security.