The court said it would examine whether the practice known as "triple talaq" is fundamental to the religion.
India is one of a handful of countries in the world where a Muslim man can divorce his wife in minutes by saying the word talaq (divorce) three times.
But activists say the practice is "discriminatory".
Many Muslim groups have opposed the court's intervention in their religious matters, although the move has the backing of the current Indian government of Prime Minister Narendra Modi.
The sensitive issue is being heard by a multi-faith bench made up of five judges - a Hindu, a Sikh, a Christian, a Zoarastrian and one Muslim.
The bench has combined several petitions from Muslim women and rights groups into one to examine the issue.
Muslims are India's largest minority community with a population of 155 million and their marriages and divorces are governed by the Muslim personal law, ostensibly based on Sharia, or Islamic law.
Even though it has been practised for decades, the unilateral instant "triple talaq" divorce finds no mention in Sharia or the Koran.
Islamic scholars say the Koran clearly spells out how to issue a divorce - it has to be spread over three months which allows a couple time for reflection and reconciliation.
Activists say most Islamic countries, including Pakistan and Bangladesh, have banned triple talaq, but it thrives in India.
In recent years, many Muslim men in India have told their wives they are divorcing them - by letter or telephone, and even by text message.
There have also been instances where Skype, WhatsApp or Facebook have been used for the purpose.