The Press Trust of India said in a report published on Monday that Sohela Ansari had told friends that her husband Aftab had uttered the word "talaq", or divorce, three times in his sleep.
When local Islamic leaders heard about the incident, they said Aftab's words constituted a divorce under an Islamic procedure known as "triple talaq".
The couple, married for 11 years with three children, were told that they had to split.
The religious leaders ruled that if the couple wanted to remarry they would have to wait at least 100 days. Sohela would also have to marry another man, spend at least a night with him and be divorced by him.
The couple, who live in the eastern state of West Bengal, have refused to obey the order, and the issue has been referred to a local family counselling centre.
India's minority Muslim population is governed by Islamic personal laws on issues such as marriage, divorce and property inheritance.
Zafarul-Islam Khan, an Islamic scholar and editor of an Islamic newspaper, The Milli Gazette, said: "This is a totally unnecessary controversy and the local 'community leaders' or whosoever has said it are totally ignorant of Islamic law.
"The law clearly says any action under compulsion or in a state of intoxication has no effect. The case of someone uttering something while asleep falls under this category and will have no impact whatsoever."
Divorce in Islam
Islamic scholars differ on whether the triple divorce pronounced concurrently by the husband is to be considered as a single divorce or three separate divorces.
"The law clearly says any action under compulsion or in a state of intoxication has no effect. The case of someone uttering something while asleep falls under this category and will have no impact whatsoever"
Zafarul-Islam Khan, Islamic scholar
If it is considered as three divorces, then the couple cannot be married again unless someone else marries the woman and chooses to divorce her.
Most scholars state that if the husband pronounces the divorce of his wife three times on one occasion, it will be counted as three divorces.
Other scholars say it should be counted as only one pronouncement of divorce.
Divorce in Islam is not decreed at all times or in all cases.
The man who wants to divorce his wife should be sober, in a well-balanced and judicious state.
If he is not fully conscious, or forced to divorce his wife, or in a state of wrath which causes him go beyond his intention and imagination and utter what he does not want to say, it is not considered valid.
Divorce in Islam should be intended and studied before considering it the only remedy for an unhappy marriage.