The law would give the government the power to shut down media outlets it finds guilty of racism.
President Evo Morales says it will help reverse centuries of discrimination against Bolivia's indigenous majority.
The papers are not opposed to the racism law in its entirety.
But they say articles which let the government punish journalists and fine or shut media that publish what it considers to be "racist and discriminatory ideas" could be misused to stifle political criticism.
Among the papers involved in the protest are El Deber of Santa Cruz, La Prensa of La Paz, and Los Tiempos of Cochabamba.
No pretext
Mr Morales, Bolivia's first indigenous president, has rejected the concerns, saying he is determined to approve the law without modifications.
He said freedom of expression was protected, but could be used as a pretext for racism.
"The time has come to eliminate the practice of racism in Bolivia because it is the most undemocratic practice in the world as it does not respect equality between citizens," he said.
The anti-racism law is supported by organizations representing Bolivia's indigenous communities, which have suffered severe discrimination dating back to the Spanish colonial era.
The legislation is being considered by Bolivia's senate, where Mr Morales's supporters have a majority.
BBC News
