Peek, the third person to occupy the job in the last year, was escorted off the White House grounds on Friday, that source and a separate source also told CNN.
Peek had only worked in his NSC position for several months. He formerly worked at the State Department as the Deputy Assistant Secretary of State for Iraq and Iran.
CNN has reached out to Peek for comment but has not heard back.
Axios first reported Peek had been placed on administrative leave pending a "security-related investigation."
Peek was scheduled to accompany President Donald Trump on his trip this week to Davos, Switzerland, for the World Economic Forum but was removed from the trip last week, two sources told CNN.
A National Security Council spokesman did not have a comment, saying "We do not discuss personnel matters."
Peek's position -- and the previous two people to hold it -- have been at the center of the ongoing impeachment investigation of Trump's Ukraine conduct.
Peek had replaced Tim Morrison, who left the position last year before testifying in the House impeachment inquiry that he was told Trump wanted a top Ukrainian official to announce an investigation that would help the President politically before US security aid to Ukraine would be released.
Morrison had replaced Fiona Hill after she left the post last summer. Hill told lawmakers during her House impeachment inquiry testimony that US Ambassador to the European Union Gordon Sondland was involved in a "domestic political errand" in Ukraine, while she and others were trying to stay involved in "national security foreign policy."