Violence was also reported in Mumbai, the Maharashtra state capital, where protestors were seen closing shops and clashing with police in several areas of the city.
Protesters blocked traffic, stoned buses and set fire to train coaches.
Curfews have been imposed in some towns. State authorities played down the violence, calling the rioting "sporadic incidents".
R R Patil, Maharashtra deputy chief minister said: "Some people have reacted to the statue desecration episode, but now the situation is okay and people are cooperating."
Low-caste Hindus, also know as "dalits", make up about 16 percent of India's 1.1 billion population, and are at the bottom of the 3,000-year-old Hindu caste hierarchy.
Ambedkar was one of the main architects of India's democratic constitution that prohibits discrimination on matters of caste.