This is a strange one.
I would suspect warped brakes but it should still cause some feeling even at low speeds. Does the car kind of jerk to a stop when coming up to a stop light? as if you were pressing and letting go of the brake slightly? The low speed vibrations could be masked by power steering especially if that power steering is drive by wire.
another way to check is jack up the front of the car and have someone lightly touch the brake just enough so you can spin the tire by hand but the brake still rubs. if it gets harder and easier than it is definitely a warped disk.
it could be the torque from the brake is loading up a suspension part and letting go. To check this see if any rubber suspension pieces are bad or if anything is loose looks worn or feels worn.
Check to make sure the caliper and pads are installed correctly and bolted down tight.
Lastly it could be your ABS especially if you are braking hard. but it could be malfunctioning or stuck in some safety mode. I would expect the ABS light to turn on on your dash if this was the case.
Last thing is it could be the cv joint in one of your axle shafts is worn out. when the car is putting power into it it will tighten up and might center itself where it is balanced but when you are coasting or applying brakes it could fall into a different position where it is no longer centered causing a vibration.