Tata was not present for Miller's Wednesday visit to Fort Bragg, N.C., and the USS Gerald R. Ford aircraft carrier, where the secretary's chief of staff Kash Patel was also present, according to Bloomberg, which first reported the diagnosis.
Tata was one of the several senior US defense officials who met on November 13 with Lithuanian Defense Minister Raimundas Karoblis, who had contracted the virus.
Hoffman said the department is doing contact tracing and conducting rapid testing for those who came in contact with the delegation.
Tata, a retired brigadier general, is the latest in a series of senior military officials who have tested positive for the disease. Lewandowski said he believed he contracted the virus in Philadelphia while assisting the president's election challenge there.
Last month nearly all of the US military's Joint Chiefs of Staff went into self-quarantine after two senior military officials who attended a top-level meeting tested positive for COVID-19.
The statement only said Tata had become ill.
Mr. Tata has been performing the duties of Undersecretary of Defense for Policy since Secretary of Defense Mark Esper and several other top officials in the Department of Defense were ousted last week.
But Anthony Tata, who President Donald Trump installed earlier this month to serve as undersecretary of defense for policy, also joined the meetings, and he showed positive for coronavirus in two tests taken Thursday.
Hoffman said Miller and the service secretaries aren't going to quarantine "based on testing and mitigation measures that were in place during the Lithuanian delegation's visit and CDC guidelines".
The report comes just over a month after an outbreak among top Pentagon officials that required several members of the Joint Chiefs of Staff to self-isolate after Coast Guard vice commandant Adm. Charles Ray tested positive.