The spat became public after superstar Karishma Kapoor was dragged to court by her industrialist husband, Sunjay Kapur.
He asked the Delhi High Court to stop her taking their five-month-old daughter overseas, as he feared she would not bring her back.
Million of Indians have been glued to their TV sets and newspapers have been carrying front-page articles.
A leading dairy company has even used the split in an advertisement for its butter.
One TV news channel asked its viewers to participate in a poll on whether the couple should stay together.
"My wife has been deliberately and without any reason depriving our minor daughter of my care and company," Kapur said in his petition to the court.
But the actor says he deserted her.
"(Sunjay's) petition is nothing but a crude attempt to urge and seek redress of matrimonial issues ... by using the minor as a pawn," Kapoor's petition said.
Kapoor, 31, says she was taking the baby along on a foreign trip and had no plans to settle overseas.
The couple who were childhood friends married in September 2003, amid splendor and national media attention but drifted apart this year. Local television and newspapers said there were rumours he had an affair.
Kapoor, moved back to her own house in Mumbai from her husband's home in New Delhi and gave birth to Samaira in March. She had Samaira's passport made after she told authorities that she lived separately from her husband.
But Kapur, a US national, went to court saying his rights as a father had been violated as he had no knowledge of the baby's travel plans nor had he given his consent.
A judge has ordered them to try and resolve their problems. Under Hindu law -- both parents have equal rights over their children.