Drought stress imposes severe constraints on crop growth and yield. The NAC transcription factors (TF) play a pivotal role in regulating plant stress responses. However, the biological functions and regulatory mechanisms of many cotton NACs have not been explored. In this study, we report the cloning and characterization of GhNAC2-A06, a gene encoding a typical cotton NAC TF. The expression of GhNAC2-A06 was induced by PEG treatment, drought stress, and ABA treatment. Furthermore, we investigated its function using the virus-induced gene silencing (VIGS) method. GhNAC2-A06 silenced plants exhibited a poorer growth status under drought stress conditions compared to the controls. The GhNAC2-A06 silenced cotton plants had a lower leaf relative water and chlorophyll content and a higher MDA content compared to the controls under the drought treatment. The levels of superoxide dismutase (SOD), peroxidase (POD), and catalase (CAT) enzyme activity in the GhNAC2-A06 silenced plants were found to be lower compared to the controls when exposed to drought stress. Additionally, the downregulation of the drought stress-related genes, GhSAP12-D07, GhNCED1-A01, GhLEA14-A11, GhZAT10-D02, GhPROT2-A05, GhABF3-A03, GhABF2-D05, GhSAP3-D07, and GhCPK1-D04, was observed in the GhNAC2-A06 silenced cotton. Together, our research reveals that GhNAC2-A06 plays a role in the reaction of cotton to drought stress by affecting the expression of genes related to drought stress. The data obtained from this study lay the theoretical foundation for further in-depth research on the biological function and regulatory mechanisms of GhNAC2-A06.