The pipeline of current robotic pick-and-place methods typically consists of several stages: grasp pose detection, finding inverse kinematic solutions for the detected poses, planning a collision-free trajectory, and then executing the open-loop trajectory to the grasp pose with a low-level tracking controller. While these grasping methods have shown good performance on grasping static objects on a table-top, the problem of grasping dynamic objects in constrained environments remains an open problem. We present Neural Motion Fields, a novel object representation which encodes both object point clouds and the relative task trajectories as an implicit value function parameterized by a neural network. This object-centric representation models a continuous distribution over the SE(3) space and allows us to perform grasping reactively by leveraging sampling-based MPC to optimize this value function.