We study wakes and gap opening by low mass planets in gaseous disks in the presence of magnetohydrodynamical (MHD) turbulence driven by the magnetorotational instabilty (MRI), using three dimensional simulations in the unstratified local shearing box approximation. Density wakes propagating in MRI turbulent disks steepen into shocks, similar to the planetary wake steepening in inviscid HD disks. Angular momentum deposition by shock damping opens a gap in the disk, even for low mass planets in both MHD turbulent disks and inviscid hydrodynamic (HD) disks, in contradiction to the ``thermal criterion'' for gap opening. We test the ``viscous criterion" for gap opening by comparing gap properties in MRI-turbulent disks to HD flows in which there is a kinematic viscosity with the same total stress. In MHD disks with net vertical magnetic fields, the planet-induced gaps are significantly deeper than those in viscous disks. This difference arises due to the weak dependence of the Maxwell stress on the density across the gap, or equivalently the effective $\alpha$ is higher within the gap region in MHD disks. In MHD disks with net toroidal magnetic fields, the gap depths are closer to those in viscous cases, but within the horseshoe region the MRI is suppressed. In both cases, the effective value of $\alpha$ is not constant across the gap region. We also find that magnetic fields can strongly affect the gas flow in the circumplanetary region. We confirm previous results that there is a large excess torque close to the planet in MHD flows, and we find that long-lived density features (termed zonal flows) produced by the MRI can affect the one-sided torque. Taken together, these results call into question the use of a constant $\alpha$-viscosity to model gaps in protoplanetary disks.
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