State police have arrested more than 2,400 people since Friday.
This includes husbands and relatives of alleged child brides, as well as priests who officiated the marriages.
BBC reports Opposition leaders have called the drive a "farce", alleging it disproportionately targets Muslims.
But Chief Minister Himanta Biswa Sarma says that his government's "war" is against child marriage and doesn't target one community.
It is illegal for girls under the age of 18 to marry in India, but the practice still continues in many parts, mainly due to patriarchal traditions and poverty.
According to government data, more than two out of 10 girls are married before the age of 18.
India's parliament is considering a bill that could increase the minimum age of marriage for women to 21 years.
But among Muslims - who mostly get married under the Muslim personal law - girls can get married once they attain puberty. The National Commission for Women has also approached the Supreme Court, asking for the marriage age for Muslim women to be made on par with that of other religions.
The Bharatiya Janata Party, to which Mr Sarma belongs, has been pushing for a uniform civil code, which will apply to all citizens.
Since the arrests began on Friday, female relatives of the arrested men have been protesting outside police stations. Many women say that the arrested men are the primary breadwinners of their families and they are completely dependent on them. The government has said it will give financial assistance to the affected women, but that hasn't assuaged their fears.
"I am worried about how I'm going to look after my child," one woman told The Indian Express newspaper.
"My husband works in the fields and I'm completely dependent on him," said another woman, adding that she only had basic primary education and didn't know how to access legal help.
On Saturday, police in Dhubri district beat protesters and used teargas to disperse them, the Times of India newspaper reported.
Police have invoked the Protection of Children from Sexual Offences (Pocso) Act against men accused of marrying girls below 14 years of age - punishment ranges from seven years' imprisonment to a life sentence and the accused can't get bail.
Those who allegedly married girls between the ages of 14 and 18 are being charged under the Prohibition of Child Marriage Act, which carries a maximum sentence of two years' imprisonment and a fine of 100,000 rupees ($1,213; £1,005).
Mr Sarma said more than 8,100 people had been named in police complaints so far, including the parents of grooms and priests who performed the marriage ceremonies. He said he had asked the police to act with "zero tolerance".
To save thousands of girls from child marriages in the future, "one generation will have to suffer", he said last week as the crackdown began.
But opposition leaders say the government is making life more difficult for ordinary people.
Ripun Bora, leader of the Trinamool Congress party, called the crackdown "whimsical" and said the state government was misusing the law.
Gaurav Gogoi, a lawmaker from the Congress party, called the move a "[public relations] exercise", saying police were investigating cases that were "decades old without proper enquiry or adherence to procedure".
Mr Sarma, however, has said the crackdown on child marriage will continue till 2026, when the next state elections will be held.