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".
"US citizens who wish to depart India should take advantage of available commercial transportation options now," it said.
Some US citizens have reported being denied entry to hospitals due to a lack of space, it added.
The warning comes as the White House said the US is redirecting its own order of the supplies needed to make the AstraZeneca, allowing India to make more than 20 million doses for its own use.
The US is also sending more than $100m in supplies to India, including almost one million instant tests on a first flight.
The Indian government has welcomed what it called an "outpouring of solidarity" from around the world, with more than 40 countries pledging urgently needed equipment.