Gross said when Google has "clear warning signs" about hackers, the company puts in place "extra roadblocks to thwart these bad actors."
He said the warning does not mean that a person's email account has been hijacked, but it does mean that Google suspects government actors have targeted the account.
He encouraged users to take extra steps to protect their information, such as using strong passwords and enabling two-step verification.
According to Foreign Policy magazine, which first reported the news, the warning system will make it more difficult for authoritarian regimes to hack into the private communications of activists.
The magazine reported that the warning system is not aimed at any particular country and that Google has no plans to release data on which countries hack into their citizens' emails the most frequently.
But the move comes amid tensions between Google and the Chinese government.
Last week, Google announced that it would begin alerting Chinese users when they enter search terms that might draw the attention of Chinese censors.
Although the company was careful not to explicitly blame the Chinese government, it noted that users regularly receive error messages when they search for certain politically sensitive terms.
In 2010, Google stopped censoring search terms on its Chinese site and moved much of its Chinese operations to Hong Kong, Foreign Policy noted.
That move followed a series attacks, widely believed to be the work of the Chinese government, on the Gmail accounts of human rights activists.
–Updated at 4:25 p.m.