Warner revealed on Monday she was abused by a member of the crowd in Adelaide last week while walking to meet her husband and Australian opener David in the players' area.
The incident prompted her to confront a group of males while she had two of her daughters, aged three and eight, with her.
CA have since contacted her offering extra security at the remaining three Tests of the summer, against South Africa.
Warner has opted not to have physical security surround her, but instead has been given a number to call if any further abuse is directed at her.
"I just said, 'Look it's unnecessary, I don't need an escort. I'm very independent and I can stick up for myself'," she told Triple M Summer Breakfast.
"But it's more about the safety of all the players and their partners and families, and just everyone in general.
"As a mum of three daughters, their safety is paramount."
Warner stressed she was not receiving special treatment and that the abuse had not centred around her husband David.
"I have a phone number I can call, as can everyone else," Warner said.
"It's not just a phone number for me or the Warners.
"This was a personal attack on me. It's got nothing to do with Dave, it's about my past and about me."
Saturday's first Test at the Gabba will be the two teams' first red ball match since Australia's 2018 tour of South Africa, where Mrs Warner was the subject of concerted crowd abuse which drew widespread media attention.
A Cricket South Africa official who posed for a photo with fans who targeted the former ironwoman in Port Elizabeth later resigned.
Warner admitted she was nervous about the prospect of a repeat of 2018.
"It does concern me, it does make me a little nervous," she said.
"But I am sure being in Australia that won't happen."
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