The stay-at-home mum's petition, launched on Saturday night, attracted hundreds of signatures within hours, and what she called a "passionate" public response.
She said councils should consider provisions for shade at any new playground.
Mrs Foy, of Mangere, said the quality of playgrounds across Auckland and New Zealand varied widely but even some new playgrounds had no cover.
"Things like this I feel should be looked at ... There needs to be some sort of consideration for children and the heat."
She said the issue was an especially hot topic on Saturday, "a prime example because it was a scorcher".
Mrs Foy said the "slip, slop, slap" sun-protection mantra did not cover all risks children faced in exposed playgrounds. "When that sun is just beating down, and it's relentless, there's no shade, then it can start to affect them ... overheating, dehydration. So it's more than just about getting burned.
"This is not limited to Auckland City residents ... once this gets going this needs to be mandatory across New Zealand," Mrs Foy's petition added.
Auckland Council operates more than 700 playgrounds.