To respond to the demands of industrial advancement in terahertz (THz) telecommunications, especially in 5G and 6G telecommunications, and considering the rapid progress in other sectors, scientific research and innovation have found nanoantennas to be the most effective component for the transmission and reception of electromagnetic waves in the THz band with enhanced efficiency. It is essential for determining a directional, flexible, smaller antenna. Due to its exceptional characteristics, the terahertz (THz) range of the electromagnetic spectrum presents numerous development opportunities in diverse applications, such as telecommunications, particularly in 5G and 6G, imaging, non-destructive testing, safety control applications, and process control. This study is based on a rectangular nanoantenna with a silicon dioxide substrate of dimensions 100 × 63 × 10 µm3 with a relative permittivity ( \({{\varvec{\varepsilon}}}_{{\varvec{r}}}\) = 4). The antenna is designed with a rectangular patch having a 30 × 22 µm2 dimension and a 5 nm thickness, and investigates how varying the patch antenna materials as copper and graphene. The simulations were conducted using the Ansys High-Frequency Structure Simulator (HFSS) to analyze site parameters, including the reflection coefficient (S11), voltage standing wave ratio (VSWR), and gain. The results show that graphene is the best material, in terms of performance and efficiency in the THz frequencies. We achieved an excellent performance from the rectangular nanoantenna at 7.81 THz, with an S11 of −50.40 dB and a VSWR of 1.006.