The Lok Sabha had last week passed the bill that makes triple talaq punishable by up to three years imprisonment for the husband.
IUML leader in the Lok Sabha PK Kunhalikutty alleged there were many "lacunae" and "contradictions" in the bill passed by the Lower House last week.
IUML national general secretary said various Muslim bodies in the country would move the Supreme Court if the bill was also passed by the Rajya Sabha.
"We will challenge it in the Supreme Court. We will move the apex court if the Rajya Sabha also passes the bill. The IUML will be a party to it," Mr Kunhalikutty told PTI.
Hitting out at the BJP government, he alleged the ruling party's move to "criminalize a family problem is completely politically motivated".
"It is a bid (by the Centre) to interfere in the personal law," the IUML leader said.
Alleging there were lacunae in the bill, he said it does not answer many fundamental questions, including protection of the wife and children if the husband goes to jail for uttering "talaq" three times.
He also claimed that the practise of triple talaq does not exist in the country.
The bill will now be sent to the Rajya Sabha for passage before it is forwarded to the President for signing it into law.
Given the Congress's stated support, the bill is likely to be passed by the Rajya Sabha, where the government lacks a majority.
The Supreme Court had outlawed instant triple talaq in August and asked the government to frame a law within six months.
Ending the controversial divorce practice was one of the ruling BJP's electoral promises.
Members from RJD, AIMIM, BJD, AIADMK and All India Muslim League had opposed the bill, saying it was arbitrary in nature and a faulty proposal.
ET Mohammed Basheer of the IUML and Asaduddin Owaisi of the AIMIM had alleged that through the bill the government was trying to bring in a Uniform Civil Code.