Proton magnetic resonance spectroscopic imaging (1H-MRSI) is a powerful tool that enables the multidimensional non-invasive mapping of the neurochemical profile at high resolution over the entire brain. The constant demand for higher spatial resolution in 1H-MRSI has led to increased interest in post-processing-based denoising methods aimed at reducing noise variance. The aim of the present study was to implement two noise-reduction techniques, Marchenko–Pastur principal component analysis (MP-PCA) based denoising and low-rank total generalized variation (LR-TGV) reconstruction, and to test their potential with and impact on preclinical 14.1 T fast in vivo 1H-FID-MRSI datasets. Since there is no known ground truth for in vivo metabolite maps, additional evaluations of the performance of both noise-reduction strategies were conducted using Monte Carlo simulations. Results showed that both denoising techniques increased the apparent signal-to-noise ratio (SNR) while preserving noise properties in each spectrum for both in vivo and Monte Carlo datasets. Relative metabolite concentrations were not significantly altered by either method and brain regional differences were preserved in both synthetic and in vivo datasets. Increased precision of metabolite estimates was observed for the two methods, with inconsistencies noted for lower-concentration metabolites. Our study provided a framework for how to evaluate the performance of MP-PCA and LR-TGV methods for preclinical 1H-FID MRSI data at 14.1 T. While gains in apparent SNR and precision were observed, concentration estimations ought to be treated with care, especially for low-concentration metabolites.