Mr Palmer says the tax is bad for the national economy, but it won't affect him directly.
"It probably won't cost me anything because I'm not mining anything that comes under the classification of it," he told reporters in Brisbane on Tuesday.
Mr Palmer said while he would not take out an injunction, West Australian mining magnate Andrew Forrest was planning to challenge the tax in court.
"Certainly Andrew Forrest's indicated he'll do that," he said.
"He's got major concerns with it because it affects him, it affects his business and it affects the ability of his workers."
The mining executive attacked the tax, saying it was another barrier to Australian businesses in the global economy.
"We're competing against the United States, we're competing against Europe," he said.
"A lot of these things are put up as barriers to Australian industry so we become less competitive."
Mr Forrest's company Fortescue Metals confirmed on Tuesday it had engaged senior counsel for a High Court challenge to the Minerals Resource Rent Tax.
Mr Palmer last week announced plans to mount a court challenge against the federal government's carbon emissions tax.
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