Trump's team may have intentionally concealed classified documents when agents tried to retrieve them in June.
If the special master decides that some material is covered by Trump's claims of executive privilege, it could hinder the government's investigation.
Cannon, who was appointed in 2020 a few months before Trump stepped down, rejected the government's argument.
The records belong to the government and that Trump is no longer president and therefore cannot claim executive privileges.
He gave Trump's legal team and the Justice Department until Friday to jointly file a proposed list of special master candidates.
The one the court eventually taps would require the requisite security clearance and legal expertise.
It is unclear whether the Justice Department will appeal against Canon's decision or on what grounds.
"The United States is investigating the opinion and will consider appropriate next steps in the ongoing trial."
Justice Department spokesman Anthony Cooley said. Representatives for Trump did not respond to a request for comment.
"Remember, fighting 'justice' and a corrupt department of the FBI requires courage and 'daring'."