The Snapchat-like feature also lets people playfully drawn on or add text to images, which are presented in a slide-show style once posted.
Instagram account settings allow users to dictate whether stories should be viewable only by followers, and opt to conceal them from some.
Snapchat, which has more 100 million users, is known for automatically making postings disappear after 24 hours. However, the company released a feature in July called "Memories" that enables users to save and share content.
Instagram said the new feature does not allow users to "like" an image or post a comment, but followers can send direct messages to the uploader.
Instagram Stories will be rolling out globally over the next few weeks on Apple's iOS and Google's Android platforms.
Instagram on Monday said separately that is adding a new weapon for fighting harassment at the popular mobile app.
The social network began letting some accounts that attract torrents of feedback filter those comments by keywords or even turn off the option to comment on particular posts.
If the test goes well, the anti-harassment feature could begin to spread across Instagram in coming weeks.