Single crystals of MgCNi3, with areas sized up to 1 mm(2), were grown by the self-flux method using a cubic anvil high-pressure technique. In low applied fields, the dc magnetization exhibited a very narrow transition into the superconducting state, demonstrating good quality of the grown crystals. The first critical field H-c1, determined from a zero-temperature extrapolation, is around 18 mT. Using the tunnel-diode resonator technique, the London penetration depth was measured with no applied dc field and the Campbell penetration depth was measured with the external dc fields up to 9 T for two different sample orientations with respect to the direction of applied magnetic field. The absolute value of the London penetration depth, lambda(0) = 245 +/- 10 nm, was determined from the thermodynamic Rutgers formula. The superfluid density, rho(s) = lambda(0)/lambda(T), was found to follow the clean isotropic s-wave behavior predicted by the weak-coupling BCS theory in the whole temperature range. The low-temperature behavior of the London penetration depth fits the BCS analytic form as well and produces a value close to the weak coupling one of Delta(0)/(k(B)T(c)) = 1.71. The temperature dependence of the upper critical field H-c2 was found to be isotropic with a slope at T-c of -2.6 T/K and H-c2(0) approximate to 12.3 T at zero temperature. The Campbell penetration depth probes the vortex lattice response in the mixed state and is sensitive to the details of the pinning potential. For MgCNi3, an irreversible feature has been observed in the TDR response when the sample is field cooled and warmed versus zero-field cooled and warmed. This feature possesses a nonmonotonic field dependence and has commonly been referred to as the peak effect. It is most likely related to a field-dependent nonparabolic pinning potential. DOI: 10.1103/PhysRevB.87.094520