The health board has a budget for the project of just under $4 million, with the rest of the funding coming from other sources.
Council chief operating officer Dave Foster said the proposed hub was aimed at improving library services.
"We need to ensure we're meeting the needs of current and future library users," he said.
Mrs Michie said those signing the petition were of all ages and ethnicities and had four major concerns - the amount of ratepayer money being spent, the possible reduction in books, access issues for the elderly, disabled and young families, and the availability of parking.
Petition signatory Joan Taikato said there were other places a heath hub could go and it was "not part of the council's mandate". She said the health of children was the government's responsibility, not the ratepayers'.
Mrs Michie said she would be outside the library tomorrow, and on Tuesday and Thursday next week.
Mr Foster said the footprint of library services within the building would change - from 4400sq m to 4000sq m.
"The library does not currently occupy all of the building it's in - the third floor is currently not used by the library.
"Lakes District Health Board would be coming in as a tenant and paying for its share of the refit. The council and ratepayers will not be paying for health services."
Mr Foster said the library building needed maintenance and upgrading, including long-standing issues with the roof, ceilings and carpet, and earthquake strengthening.
"People also seem to be under the misunderstanding that we're reducing our library stock to make room for this project. That is incorrect.
"We are constantly withdrawing books as new ones are purchased and periodically have a more thorough clean out."
He said the project was still at concept stage and all cost estimates and plans to date were concept only and subject to change.
"We would encourage people to visit the council's website for information about what's proposed."
- For information visit www.rotorualakescouncil.nz, click 'Rotorua 2030', 'Portfolios, People', 'Library and Child Health Hub' project page.