Mata Amritanandamayi, who blesses her devotees with a hug, escaped unhurt in the attack which took place in Kerala.
Reports say her followers wrestled the attacker on to the ground before he could reach the stage where she was leading prayers for 18,000 people.
She has a huge following in India and supporters around the world.
'I don't want my [followers] to create any problem for what had happened' - Mata Amritanandamayi
The incident took place in Kerala's in Kollam district, where Ms Amritanandamayi's group is based.
Two of her followers are said to have suffered minor injuries in the attack.
"I heard someone shouting, I couldn't see his face," she told Indian television channel, NDTV.
"He had a knife in his hand."
The Indian Express newspaper said the attacker may have been a follower who was expelled recently.
Ms Amritanandamayi said on Monday she wanted her followers to forgive the attacker.
"All those who are born will die one day. I am going ahead keeping this reality in mind," she said.
"I will carry on. I will continue to give darshan to the devotees coming here to meet me. I don't want my [followers] to create any problem for what had happened yesterday."
Known to her followers as "Amma" (Mother), Mata Amritanandamayi, 51, heads a charitable trust which runs schools and hospitals across India and abroad.
Ms Amritanandamayi, whose name means "Mother of Absolute Bliss" was born to a low caste family in a southern Indian fishing community.
She refused school and then marriage, preferring to meditate. She began hugging devotees at a young age.
In the 1980s Ms Amritanandamayi founded an ashram, or spiritual home, to receive followers and dispense more hugs.