The Dutchman announced the decision following the Italian Grand Prix on Sunday, citing private reasons.
Albers, who only took charge of the team in July following a takeover by a group of investors advised by former F1 team principal Colin Kolles, will be replaced by deputy Manfredi Ravetto.
In a statement, Albers said: "Over the past months I have dedicated all my energy to ensure the takeover of the team would go as smoothly as possible and to achieve the best possible result for our investors, sponsors and all the people involved with Caterham F1 Team.
"As such, I worked tirelessly to reconstruct the team while, at the same time, making technical updates on the car.
"In doing this we created both a better foundation for the team's future and achieved significant improvements on the speed of the car.
"Due to private reasons and in order to be able to spend more time with my family, I will resign from my position as CEO of Caterham F1 Team. I wish the team all the best in the future."
Ravetto added: "Christijan has been an asset to the team since the moment he joined. It's been a challenging last few months, but we have moved forward together and we want to thank him for his hard work and commitment to the team. We wish him the best for the future."
Caterham have yet to win a point in the constructors' championship so far this season, with drivers Kamui Kobayashi and Marcus Ericsson finishing 17th and 19th respectively at Monza.