Mr Miller, who has been self-isolating for the past five days, confirmed he had contracted coronavirus on Tuesday, BBC reported.
Top US General Mark Milley and other military leaders are also quarantining after Coast Guard official Admiral Charles Ray tested positive.
Other officials are self-isolating “out of an abundance of caution”.
Adm Ray, vice commandant of the US Coast Guard, is said to be experiencing mild symptoms.
While officials who attended meetings with Adm Ray last week are now quarantining, none have so far tested positive or exhibited symptoms, the Pentagon said.
It is not known how Adm Ray contracted the virus. The admiral attended an event at the White House about 10 days ago but it is not clear if he contracted the virus there or elsewhere, officials told the Associated Press news agency.
The Coast Guard said in a statement that Adm Ray tested positive on Monday and was now isolating at home. It added that any Coast Guard personnel who were in close contact with him would also quarantine.
BBC partner CBS News reported that nearly all members of the Joint Chiefs of Staff – a body consisting of senior military officials who advise the US president – were in quarantine after attending meetings with Adm Ray last week.
In addition to the chairman of the Joint Chiefs, Gen Milley, it said others in quarantine included the vice chief of staff, Army chief of staff, chief of naval operations, Air Force chief of staff, CyberCom commander, the Space Force chief, chief of the National Guard and deputy commandant of the Marine Corps.
Pentagon spokesman Jonathan Hoffman told reporters there had been “no change to the operational readiness or mission capability of the US Armed Forces.”
The Pentagon is conducting contact tracing related to last week’s meetings.
Cases rising at the White House
Meanwhile, since President Trump tested positive last week, a number of senior Republicans and others close to him have been confirmed as having the virus.
This includes First Lady Melania Trump, aide Hope Hicks, and a number of Republican senators.
Press Secretary Kayleigh McEnany has tested positive, announcing her diagnosis on Monday, and three more members of staff of the press office – Chad Gilmartin, Karoline Leavitt and Jalen Drummond – tested positive on Tuesday.
Ms McEnany was seen speaking to journalists without wearing a mask on Sunday but said no members of the press had been listed as close contacts by the White House medical unit.
Many of the people in Mr Trump’s inner circle who have tested positive attended a gathering at the White House Rose Garden on 26 September that is being scrutinised as a possible “super-spreader event”.
Another coronavirus case to emerge from that event, at which the president unveiled his nominee for the US Supreme Court, is a Christian minister from California.
Plexiglass will be used to separate Vice-President Mike Pence and Democratic challenger Kamala Harris and limit the risk of Covid transmission when they go head-to-head in a debate in Salt Lake city, Utah, on Wednesday. Both candidates have recently tested negative.
President Trump, meanwhile, returned to the White House yesterday after being hospitalised with the virus.
While at Walter Reed Medical Center, he was treated with dexamethasone – a steroid medication usually given to severe and critical Covid patients – and supplemental oxygen.