The resignations form part of a major cabinet expansion 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 from January.
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 the figures are an undercount and the real number of dead could be several times higher.
Three dozen new faces have been inducted into the new Modi cabinet, taking the number of ministers to 77, up from 52.
More than a dozen ministers are from poll-bound states such as Uttar Pradesh and Gujarat, representing different castes and regional communities, a dominant factor in India’s electoral politics.
Four members from southern Karnataka state were also added, including millionaire media mogul Rajeev Chandrasekhar, and Shobha Karandlaje, a sectarian rabble-rouser politician.
Karandlaje has several police cases filed against her over her anti-Muslim remarks.
Six other women ministers also found a place in the new cabinet.
But the expansion has witnessed the shock exit of two key members from the Modi cabinet, including Ravi Shankar Prasad — minister for law and justice and information technology — and Prakash Javadekar, minister for information and broadcasting, environment and climate change.
Both Prasad, 66, and Javadekar, 70, were seen as faces of the Modi-led Bharatiya Janata Party government, with some press reports suggesting they would handle party work ahead of the key state elections.
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’s exit from the cabinet has been particularly surprising as he was locked in a bitter dispute with foreign social media companies over a new law.
He authored a controversial law that required social media 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 over user privacy violations.
But the war of words has been sharpest with Twitter, with the microblogging site failing to appoint a permanent compliance officer based in India.
Prasad has several times publicly slammed Twitter for not following the new rules, and undermining Indian laws.
His ministry recently told a court that the social media platform does not enjoy an intermediatory status in India, making the company criminally liable for content posted on the platform.
This follows police visits to Twitter’s India office in May after the firm labelled tweets by the BJP’s national spokesman as “manipulated media”.
Twitter responded by accusing the government of “intimidation tactics”.