Aims. In this paper, we aim to measure the strength of the surface magnetic fields for a sample of five intermediate mass T Tauri stars and one low mass T Tauri star from late-F to mid-K spectral types. While magnetic fields of T Tauri stars at the low mass range have been extensively characterized, our work complements previous studies towards the intermediate mass range; this complementary study is key to evaluate how magnetic fields evolve during the transition from a convective to a radiative core. Methods. We studied the Zeeman broadening of magnetically sensitive spectral lines in the H-band spectra obtained with the CRIRES high-resolution near-infrared spectrometer. These data are modelled using magnetic spectral synthesis and model atmospheres. Additional constraints on non-magnetic line broadening mechanisms are obtained from modelling molecular lines in the K band or atomic lines in the optical wavelength region. Results. We detect and measure mean surface magnetic fields for five of the six stars in our sample: CHXR 28, COUP 107, V2062 Oph, V1149 Sco, and Par 2441. Magnetic field strengths inferred from the most magnetically sensitive diagnostic line range from 0.8 to 1.8 kG. We also estimate a magnetic field strength of 1.9 kG for COUP 107 from an alternative diagnostic. The magnetic field on YLW 19 is the weakest in our sample and is marginally detected, with a strength of 0.8 kG. Conclusions. We populate an uncharted area of the pre-main-sequence HR diagram with mean magnetic field measurements from high-resolution near-infrared spectra. Our sample of intermediate mass T Tauri stars in general exhibits weaker magnetic fields than their lower mass counterparts. Our measurements will be used in combination with other spectropolarimetric studies of intermediate mass and lower mass T Tauri stars to provide input into pre-main-sequence stellar evolutionary models.