Websites for the Indian IT ministry, the Indian Telecoms department, the Supreme Court, the Bharatiya Janata Party and the Indian National Congress were among those targeted.
Anonymous said the attacks were in retaliation against the blocking of file-sharing websites Vimeo, DailyMotion and The Pirate Bay in India.
Chennai based anti-piracy company Copyrightlabs won a court order in March which forced Indian Internet Service Providers and telephone firms to stop their customers reaching the sites to download Bollywood films.
The website of Copyrightlabs was also "down for maintenance" during the attacks.
In tweets documenting its ongoing hack attacks, Anonymous said they were being carried out in retaliation for "internet censorship" in India.
To knock out the sites, Anonymous bombarded them with data, a tactic known as a Distributed Denial of Service (DDoS) attack.
- Malinda Dharshana