The appointment in January raised fears that the circle of US intelligence chiefs was being politicised.
A White House aide said the reshuffle was not a demotion for Mr Bannon, who used to head up Breitbart News.
The aide said Mr Bannon was only given a seat on the NSC to keep an eye on National Security Adviser Michael Flynn, who was fired in February.
The NSC is the main group advising the president on national security and foreign affairs.
Palace intrigue - Anthony Zurcher, BBC News, Washington
