Officers in Uttar Pradesh state charged Shashank Yadav with spreading a rumour over oxygen shortages "with intent to cause... fear or alarm".
Yadav, who did not refer to Covid in his brief tweet, could face jail.
Uttar Pradesh is among India's worst-hit states. Its chief minister, Yogi Adityanath, is accused of downplaying the severity of the coronavirus crisis.
Earlier this week, Mr Adityanath, a right-wing ally of Prime Minister Narendra Modi, demanded that the property of anyone spreading rumours and propaganda be seized.