The process is based on allegations Dilma Rousseff broke the law in managing 2014 budget, President of the Chamber of Deputies Eduardo Cunha said.
Despite re-election in 2014, Dilma Rousseff’s popularity has slumped amid a corruption scandal involving the state-owned oil giant, Petrobras.
“I was outraged by the decision,” the president said in a televised speech.
“I haven’t committed any wrongful act,” she added.
Dilma Rousseff, who earlier called an emergency cabinet meeting, said she was confident that the impeachment motion would be rejected.
Two-thirds of the lower house must approve the process for it to proceed.
The governing coalition has a majority in the lower house of Congress.
The defeated opposition candidate in last year’s presidential election, Senator Aecio Neves, has tweeted that he supports the impeachment request.
“Everyone in the country must obey the law, especially the president,” he wrote.
Eduardo Cunha is himself facing corruption allegations, which he denies.
He has been accused of lying about a secret bank account in Switzerland.
An ethics committee is voting on whether to authorize action to eject him from his post of speaker.
Eduardo Cunha had been threatening to open impeachment proceedings if the governing party did not offer him backing.
His decision was “purely technical”, he said.
“It was a difficult decision. I did not become speaker of the Chamber of Deputies aiming to approve impeachment proceedings against the president,” said Eduardo Cunha.
The impeachment request had been filed by a distinguished jurist, Helio Bicudo, and some opposition members.
The document blames the government for the corruption scandal at Petrobras and says Dilma Rousseff violated Brazil’s fiscal responsibility laws.
In October an audit court ruled that Dilma Rousseff had borrowed money illegally from state banks to make up for budget shortfalls.
On December 1, the economy minister announced that Brazil’s economy shrank by 1.7% in the Q3 of 2015 compared with the second quarter, deepening the country’s worst recession in 25 years.
Compared with a year ago, the economy is 4.5% smaller.
The corruption scandal at Petrobras was partly to blame for the downturn, said Economy Minister Joaquim Levy.
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