, less than a millisecond. Not a camera or a human can react this quick
Humans can't, but a camera certainly could.
Note, you generally want to pre-focus the camera to eliminate the time spent focusing.
I tend to agree with AWOL that most camera shutters just won't operate in the millisecond range, particularly the common mechanical shutter. The fasterleaf shutters probably operate in the microsecond range. There are some that do for high speed movies, but they tend to be expensive.
In general most of the high speed shots (balloon popping, bullet through the card, etc.) are done by shooting in a dark room with a long shutter speed, and having a high speed flash (usually at minimal power to get the smallest amount of time) fire off while the shutter is opened. This goes all of the way back to the 1870's when Eadweard Muybridge connected many cameras to trip wires connected to flash units to prove that a horse's gallop had all 4 feet off the ground at one point.