The journalists are employees of Eleven Media, one of the country's leading news organizations, and Bertil Lintner, an expert on Myanmar's ethnic groups, The New York Times reported.
Taj Meadows, a Google spokesman in Tokyo said he could not provide specific information about the warnings or where the attacks came from.
"I can certainly confirm that we send these types of notices to accounts that we suspect are the targets of state-sponsored attacks," he said.
Meadows could not say how Google identifies a "state-sponsored" attack and could provide no other details "without giving away information that would be helpful to these bad actors."
Myanmar news publications have been highly censored during five decades of military rule, but those restrictions have been lifted since President Thein Sein came to power nearly two years ago, the Times reported.