The incorporation of crumb rubber (CR) obtained from waste tyres as a substitute for sand in concrete, resulting in the making of rubberised concrete, has led to a variety of environmental advantages and improved characteristics of the concrete. Although there have been certain enhancements, the decreased strength of rubberised concrete has restricted its wide application. This work presents an inventive technique to address this issue, integrating multiwalled carbon nanotubes (MWCNTs) to develop rubberised concrete with a compressive strength (CS) comparable to conventional mixes. Thirteen combinations were created adopting the response surface methodology (RSM). These mixtures consisted of varying quantities of MWCNTs, fluctuating from 0.05 to 0.08%, and CR substituted for 1–5% of the sand volume. The purpose of these mixtures was to determine the CS and microstructural characteristics. The finding has displayed that the CS of CR concrete is observed by 39.90 MPa, 45.49 MPa, and 57.60 MPa at 0.05% of MWCNTs and 1% of CR after 7, 14, and 28 days, respectively. Besides, the microstructural properties are getting improved while the content of MWCNTs rises in CR concrete at 28 days. It is concluded that the use of 0.05% of MWCNT along with 1–3% of CR in concrete is offering the best outcomes for the construction applications.