Turn a METAL HALIDE BULB On/Off in 1 minute Intervals?
You could build a mechanical shutter operated by a servo motor and controlled by a microcontroller easily enough, but there is another issue.

Your 400W of input power is being turned into light and heat.  I don't know what the efficiency of your proposed bulb is, but even if it was as high as 25% (dubious) you'd still need to dispose safely of 300W of heat continuously.  When the shutter obstructs the light the waste heat will probably ramp up to almost the full 400W because most of the 40k lumens are going to be converted back into heat.

Have you looked for high power LED's (or LED arrays) that can generate the kind of light intensity you need?  LED's can usually be switched on and off pretty much as required, and they're also generally more efficient than other light sources.