The proposed NIB is envisaged to act as a final body for clearing big investment proposals after which no ministry will have the power to raise objections.
According to a news report, Natarajan has said in her letter that the manner in which changes have been sought on the issue of granting project approvals was disturbing and she wondered why NIB should step in when decisions like green clearances have to be given by her ministry.
Natarajan's opposition came even as a Cabinet Note on the planned NIB was circulated to the ministries.
The Minister also said the NIB has no constitutional authority and that the proposal will decimate the role of the Environment ministry, the TV channel reported.
Concerned over delay in implementation of mega infrastructure projects, Chidambaram had recently proposed a Prime Minister-headed NIB to accord speedy clearance to big ticket projects.
The Indian industry as well as several union ministries have repeatedly complained that environmental laws and clearances are becoming an impediment in country's growth story.
Chidambaram said last Thursday that a proposal to constitute a NIB is likely to be taken by the Cabinet at its next meeting.
"(Cabinet) Note has been circulated to the ministries. We have given them a week to give their comments and it was indicated to me that it would probably come up in the next meeting of the Cabinet," he had said.
Several large projects involving investments of Rs 1.5 lakh crore are being held up because of delay in statutory clearances.
At the meeting of full Planning Commission last month, Chidambaram had proposed that the NIB's authority should extend to proposals/projects where the investment is above a certain threshold.
Earlier in June, Prime Minister Manmohan Singh had approved setting up of an investment tracking system to ensure speedy implementation of mega projects envisaging outlay of over Rs 1,000 crore.