In this study, a novel rectangular polymer single-mode optical fiber for femtosecond (fs) laser-inscribed fiber Bragg gratings (FBGs) is proposed and demonstrated. The cylindrical geometry of the widely used circular fiber elongates the fs laser beam along the fiber axis, resulting in reduced laser intensity and requiring index-matching oil immersion during FBG inscription. However, the flat geometry and negligible surface roughness of the featured fiber significantly diminish this lensing distortion and eliminate the need for oil immersion, thereby resulting in optimal focusing of the laser beam, permitting direct and efficient inscription of FBGs within the optical fiber. The core and cladding of the rectangular fiber were fabricated using two different grades of ZEONEX, a cyclo olefin polymer, which have slightly different refractive indices. The similar glass transition temperature for core and cladding simplifies the fiber drawing process, and a rectangular single-mode optical fiber with dimensions of $213\mathrm{\mu m}\times 160\mathrm{\mu m}$ and core diameter of 9.4 μm was fabricated using an in-house fiber drawing facility. A second harmonic (520 nm) fs laser beam was used to successfully inscribe a 2-mm-long FBG in the rectangular fiber within a few seconds with a point-by-point technique. The inscription of a single FBG leads to the excitation of higher order FBG peaks at 866.8 and 1511.3 nm, corresponding to widely used wavelength bands in fiber optic sensing. The strain and temperature sensitivities of the FBG were measured to be $7.31\mathrm{nm/}\%\mathrm{\epsilon }$ ($0.731\mathrm{pm}/\mathrm{\mu \epsilon }$) and 10 pm/°C, and $12.95\mathrm{nm}/\%\mathrm{\epsilon }$ ($1.29\mathrm{pm}/\mathrm{\mu \epsilon }$) and 15 pm/°C at 866.8 nm and 1511.3 nm, respectively.