The parties had combined in an attempt to block the BJP, whose campaign is being led by the Prime Minister, from winning the state.
Mr Yadav is upset that the alliance allotted his party a mere five seats to contest in Bihar. When the division of seats was first announced, the Samajwadi Party was given none. Later, Lalu Yadav said it would contest five seats, a move aimed at placating Mulayam Singh, who wanted at least 12.
Mr Yadav had earlier demonstrated his displeasure by not attending a mega rally in Patna on Sunday, addressed by Nitish Kumar, Lalu Yadav and Congress president Sonia Gandhi. He sent his brother Shivpal Yadav instead.
The Samajwadi Party has no state legislators or parliamentarians from Bihar, so the break-up's import lies in a dent to the stated unity of parties that have grouped against the BJP.
Some in Mulayam Singh's party, like Shivpal Yadav, are said to have argued that the Samajwadi Party could be seen as strengthening the BJP by walking out of the Bihar alliance. A perception that could affect the party adversely when it takes on the BJP in Uttar Pradesh, where it will seek to retain power in elections to be held in 2017.
"There is no question of any understanding with Mulayam," said the BJP's GVL Narasimha Rao as today's break-up sparked intense speculation. Mr Rao alleged that "Mulayam has distanced himself because Lalu, Nitish are losing."
Sharad Yadav of the Janata Dal United, Nitish Kumar's party, said he is confident Mulayam Singh will have a change of heart. "He is our old friend. I will meet him and resolve issues through talks," he said.
The dates for the Bihar election will be announced shortly.