OkayNG.com gathered that Systrom and Krieger have resigned from their posts as chief executive and chief technology officer respectively, not giving reasons and saying they planned to take time off.
Facebook did not respond to a request for comment, according to AFP.
Instagram in June announced it passed a billion active users, and unveiled a new long-form video feature in a bid to attract “creators” like those on YouTube.
It became the fourth Facebook platform to eclipse the billion-user mark, including the namesake social network with more than two billion users, and the messaging applications WhatsApp and Messenger.
Facebook acquired Instagram in April 2012 for a combination of cash and stock worth some $1 billion at the time.
Instagram has been a hit with young internet users, an audience that Facebook is keen to keep in its fold.
The departures come as Facebook grapples with the worst crisis in its history, vilified for not more zealously guarding information users share at the leading online social network.
Earlier this year, WhatsApp co-founder Jan Koum left Facebook, which bought the smartphone messaging service for $19 billion.
Koum said in a post on his Facebook page that he was taking time off to pursue interests such as collecting air-cooled Porsches, working on cars and playing ultimate Frisbee.
US media reports indicated that a disagreement with Facebook over the privacy of user data may have also been a factor in Koum’s decision to quit his position as a high-ranking executive and likely leave his seat on the board at the leading online social network.