India reported 379,257 new infections on Thursday, the world's highest single-day total.
The US embassy warned that "access to all types of medical care is becoming severely limited".
The level 4 "do not travel" advisory is the highest of its kind issued by the Department of State.
The overall death toll in India officially surpassed 200,000 on Wednesday, though experts believe the actual number could be much higher.
In the advisory, US citizens were told "not to travel to India or to leave as soon as it is safe to do so".