The move is part of a wider raft of measures the social media giant has taken to tackle the problem of fake news on social media.
Facebook announced in May that it would start reducing the reach of false content on Instagram and gradually extend its fact-checking partnership to include the image-sharing platform. It also said it would start blocking hashtags and posts that spread anti-vaccine misinformation. Most recently, it tightened its political advertising rules ahead of next year's US presidential election.
Launched in December 2016 following the controversy surrounding the impact of Russian meddling and online fake news in the US presidential election, Facebook's partnership now involves more than 50 independent fact-checkers in over 30 countries.
The new flagging feature for Instagram users was first introduced in the US in mid-August and has now been rolled out globally.
Users can report potentially false posts by clicking or tapping on the three dots that appear in the top right-hand corner, selecting "report", "it's inappropriate" and then "false information".
Facebook provides fact-checkers with a dashboard of flagged posts. Fact-checkers can also check content of their own choosing. They use a rating system to determine whether it contains false or misleading information.
The usual procedure on Facebook is that stories that are rated false, contain a mixture of accurate and inaccurate claims, or have false headlines will appear less prominent in users' news feeds. Accounts, pages and groups that repeatedly share misleading stories will be notified and face restrictions on distribution and their ability to make money from advertising.
Instagram's new flagging tool uses a similar dashboard and rating system. Posts rated as false by fact-checkers will be downgraded on its hashtag search and explore pages, two big methods people use to find new posts on the platform.
Facebook says that if a fact-checker rates a story as false on Facebook and it then appears on Instagram, an extra button can be clicked to rate it on there as well.
One notable difference is that an Instagram user whose content is reported and rated will not be notified.
Stephanie Otway, a spokeswoman for Instagram, said: "This is an initial step as we work toward a more comprehensive approach to tackling misinformation."