The photo-sharing site did not give any explanation for the resignations.
In a statement, Zuckerberg described the two as "extraordinary product leaders".
"I've learned a lot working with them for the past six years and have really enjoyed it. I wish them all the best and I'm looking forward to seeing what they build next," Zuckerberg said.
Facebook had brought Instagram six years ago for $1 billion, the photo app had passed a billion active users in June. However, there have been reports of frequent clashes with Facebook Chief Executive Mark Zuckerberg over the direction of Instagram.
WhatsApp co-founder Jan Koum and co-founder Brian Acton had left Facebook earlier this year, which was bought by Zuckerberg's company for a record $19 billion.
Instagram's revenue this year is likely to exceed $8 billion, showed data from advertising consultancy EMarketer.
In India, both Facebook and Whatsapp have come under scanner after the Department of Telecom (DoT) sought to block the social sites citing national security issues. There have been growing concern over privacy issues after Facebook had declared 87 million users' data was hacked by Cambridge Analytica earlier.
The Indian government had told Whatsapp it was dissatisfied with the messaging app over steps taken by it to stop fake news and rumours triggering mob violence. Facebook is also facing multiple inquiries from US and British regulators about the Cambridge Analytica user data scandal.