The 46-year-old, who is back with her ninth album, Such Pretty Forks In The Road, disliked the song at first and did not want it to feature on the record.
However, the Canadian singer was convinced by her close friends and the track became one of her most well-known.
Isn't this ironic, don't you think?@Alanis reveals which track was nearly left off 'Jagged Little Pill.' #TheOneShow | @MissAlexJones | @gethincjones pic.twitter.com/CHsN4wMuwp
— BBC The One Show (@BBCTheOneShow) August 5, 2020
Speaking on The One Show via video call, she said: “I wrote Ironic with (producer) Glen Ballard very early in the writing of the record, and it was not autobiographical, it was us just trying to entertain each other.
“We were being really loose and quick with everything.
“When it came time to decide what was on the record, I didn’t want Ironic on the record but those around me who I trusted really loved the song.
“So it wound up being on the record – but it was a close call.”
Morissette also suggested that the Broadway rock musical based on the album could transfer to the West End when theatres reopened following the coronavirus pandemic.
Asked whether they aimed to perform in London, she said: “Heck yes, London is a dream goal.”
Morissette also recalled being robbed at gunpoint when she first moved to Los Angeles in the 1990s, nearly losing all the material for the Jagged Little Pill album.
She said: “I was writing for the record and I had my backpack full of music and lyrics and, if you can forgive the datedness of this, some cassette tapes.
“All of a sudden, I went out to get running shoes and I drove home and I turned around and I was being held up at gunpoint.
“They wanted all my things and I knew I was going to give them anything, first of all, but second of all I had my backpack with the whole Jagged Little Pill content in it.
“I gave them my wallet and purse and they said ‘Go lie down’ so I lay down with my backpack and I thought maybe they would grab that on the way out, but they didn’t.”