Nightingale, who has been in the role for a year, will leave at the end of the month. He will be replaced by his deputy, Chris Bennett.
Chief executive Andrew Swaffield said: “Over the last year, Barry has led his team to ensure that the business turned a corner financially, making considerable contributions to our financial strategy and ensuring that long-term aims are achieved.
"I would like to take this opportunity to wish him the very best for the future and thank him for his contribution to the business.”
Bennett has previously worked for both British Airways and easyJet. He joined Monarch Airlines as finance director in 2010.
“Monarch has turned a corner and I am looking forward to being part of the exciting story that is unfolding across the business with a refreshed cost-efficient focus on our customers.,” he said.
Nightingale said he was leaving to “pursue new challenges”. He joined the business from gambling firm Betfred and had previously worked for Airtours.