In a blog post, the US search giant said that it is "constantly on the lookout for malicious activity" on its systems, particularly unauthorised accessing of personal email accounts.
Google said that where there is "specific intelligence" from monitoring activity or warnings from users, it will "put in place extra roadblocks to thwart these bad actors".
This has now been expanded to include measures to protect a "subset of our users", who Google believes "may be the target of state-sponsored attack".
It is thought that the move is particularly designed to protect activists, journalists and political figures who could be targeted online.
These users will see a warning on their account, saying: "We believe that state-sponsored attackers may be attempting to compromise your account or computer."
The users will be urged to take steps to better protect themselves and their account, such as creating a more secure password containing capital and lower case letters.
Google will also offer a two-step verification process for security, while users can update their browser, operating system, plugins and documents editors to increase protection.
"Attackers often send links to fake sign-in pages to try to steal your password, so be careful about where you sign in to Google and look for https://accounts.google.com/ in your browser bar," said Eric Grosse, Google's vice president of security engineering.
"These warnings are not being shown because Google's internal systems have been compromised or because of a particular attack."
Google said that it was unable to go into detail about why it knows specific activity is state-sponsored "without giving away information that would be helpful to these bad actors".
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But the company said that its detailed analyses, including victim reports, often "strongly suggest the involvement of states or groups that are state-sponsored".
"We believe it is our duty to be proactive in notifying users about attacks or potential attacks so that they can take action to protect their information. And we will continue to update these notifications based on the latest information," Grosse added.
Some users have already reported receiving the warning, including Marc Ambinder, an American journalist specialising in US national security and politics.
After getting the warning, he tweeted: "Google sends me this message: '...state-sponsored attackers may be attempting to compromise your account or computer'. Thanks, China."