Potassium (K) is an indispensable nutrient element in the development of fruit trees in terms of yield and quality. It is unclear how a stable or unstable supply of K affects plant growth. We studied the root morphology and physiological and molecular changes in the carbon and nitrogen metabolism of M9T337 apple rootstock under different K levels and supply methods using hydroponics. Five K supply treatments were implemented: continuous low K (KL), initial low and then high K (KLH), appropriate and constant K (KAC), initial high and then low K (KHL), and continuous high K (KH). The results showed that the biomass, root activity, photosynthesis, and carbon and nitrogen metabolism of the M9T337 rootstocks were inhibited under KL, KH, KLH and KHL conditions. The KAC treatment promoted root growth by optimizing endogenous hormone content, enhancing carbon and nitrogen metabolism enzyme activities, improving photosynthesis, optimizing the distribution of carbon and nitrogen, and upregulating the transcription levels of nitrogen assimilation-related genes (nitrate reductase, glutamine synthetase, glutamate synthase, MdNRT1.1, MdNRT1.2, MdNRT1.5, MdNRT2.4). These results suggest that an appropriate and constant K supply ensures the efficient assimilation and utilization of nitrogen and carbon.