The resignations form part of a major reshuffle by Prime Minister Narendra Modi ahead of seven state elections in 2022.
Health Minister Harsh Vardhan, 66, came in for particular criticism during the spike in infections in April and May.
The health service was under severe pressure in many areas with hospitals running out of beds, medical oxygen and drugs.
The Covid-19 explosion was blamed on new virus variants and the government having allowed mass religious and political gatherings to take place in January, February and March.
Modi had declared victory over the virus in January and critics say his government failed to use the time to prepare the historically underfunded health system for another wave.
India’s official death toll has exploded from around 160,000 at the end of March to more than 400,000 now, the third-highest in the world.
But many experts suspect that due to undercounting and incorrect recording of the cause of death, the real number of dead could be several times higher.
Ravi Shankar Prasad, minister for law and justice and information technology, also resigned, according to a statement from the president’s office.
Prasad, 66, a close ally of Modi, was however expected to be given an important role in Modi’s Bharatiya Janata Party (BJP) ahead of the state elections, press reports said.
Seven Indian states are due to hold elections next year, six of them currently ruled by the BJP. They include Uttar Pradesh, India’s most populous state, Gujarat and Punjab.
Earlier this year the BJP suffered a major setback when it failed to wrest power in the important eastern state of West Bengal from a high-profile Modi critic.
Some commentators said this was a reflection of Modi’s falling popularity because of his handling of the pandemic. The BJP did however retain Assam in the northeast.
Prasad has been locked in a bitter dispute in recent months with foreign social media companies.
His ministry authored rule changes that require the firms to remove and identify the “first originator” of posts deemed to undermine India’s sovereignty, state security or public order.
Social media companies and privacy activists fear the vagueness of the rules means they could be forced to identify the authors of posts critical of the government.
WhatsApp is challenging the rules in court, fearing that it will have to break its system of encryption that prevents anyone other than the sender and receiver from reading messages.
The war of words has been sharpest with Twitter, with the microblogging site failing to appoint a permanent compliance officer based in India.
In May, Indian police visited Twitter’s offices in Delhi and Gurgaon after the firm labelled tweets by the BJP’s national spokesman as “manipulated media”.
Twitter responded by accusing the government of “intimidation tactics”.
Prasad then had his Twitter account briefly locked after he posted a video containing music that breached US copyright law.
He called the move a “gross violation” and said it showed how his “calling out the high handedness and arbitrary actions of Twitter… clearly ruffled its feathers”.
The others resigning include Prakash Javadekar, minister for the environment, forests and climate change as well as information, broadcasting and heavy industries.
Ramesh Pokhriyal Nishank, minister for education, also quit.