We study the gravitomagnetism in the Scalar-Vector-Tensor theory or Moffats Modified theory of Gravity(MOG). We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency between the MOG gravitomagnetic field and that predicted by the Einsteins gravitional theory and measured by Gravity Probe B, LAGEOS and LAGEOS 2, and with a number of GRACE and Laser Lunar ranging measurements requires $|alpha| < 0.0013$. We provide a discussion.