Though Mr Systrom, in the early days of Instagram ads, famously checked each one personally to ensure it aligned with the app's aesthetics, he was not as loudly anti-ads as the founder of another popular Facebook-acquired mobile app, WhatsApp.
Systrom said the two plan to take some time off to explore their curiosity and creativity again.
The share of revenue that Instagram contributes to Facebook is set to rise from about 10% to 16%, year-over-year, according eMarketer.
Facebook shares fell 2.2 per cent, to US$161.70, at 9:44 a.m.in NY. With the founders gone, they expect Instagram will be more tightly integrated into Facebook, and may become more of a division within Facebook, rather than its own company.
"I'm looking forward to seeing what they build next", he said in a statement.
Facebook has a history of clashing with the leaders of companies it acquires.
Facebook CEO Mark Zuckerberg described Systrom and Krieger as "extraordinary product leaders".
One of the names being touted as the next boss of Instagram is Adam Mosseri.
Facebook's acquisition of Instagram, which hit 1 billion monthly users in June, has been a remarkable success.
Spokespeople for Facebook and Instagram declined to comment further on why the executives had made a decision to step down, referring back to Systrom's blog post. Facebook is under fire for its handling of users' data and its failure to halt the spread of misinformation, most notably during the United States presidential election in 2016.
Against those problems, Instagram has been one of the jewels of Facebook.
Instagram had become a key cog in the Facebook empire as the social-networking giant enjoyed seemingly unstoppable growth and a stock price that climbed steadily upward.
The news in some ways heightened Instagram's importance within the company, as its popularity among younger users is seen as more stable than at Facebook's main platform.
Systrom's fortune is valued at $1.4 billion by Forbes. Brian Acton, WhatsApp's other co-founder, had already left the previous September.
Instagram, meanwhile, has remained a bright spot for the company.