He said: "He was interviewed under caution in connection with allegations of theft.
Mr Morgan, 35, was interviewed for half an hour at Charing Cross police station on Thursday - the third anniversary of the princess's death in a Paris car crash.
The investigation, by Scotland Yard's Serious and Organised Crime Unit, concerns more than 60 letters written to Captain James Hewitt between 1989 and 1991.
Mr Morgan said the Mirror had passed the letters on to Kensington Palace after having obtained them from a close friend of James Hewitt.
"The Mirror tried to protect the name and memory of Diana from improper exploitation by James Hewitt and I am proud of having done so," he said.
A Scotland Yard spokesman confirmed that a man in his 30s had been interviewed by officers at a central London police station on Thursday.
He said: "He was interviewed under caution in connection with allegations of theft.
"He was not arrested. We do reserve the right to re-interview him in the future should it become necessary."
Mr Morgan said in a statement: "It seems a curious use of public money to deploy high-ranking detectives from the country's most important crime unit in such a matter.
"I have no criticism of the officers concerned who were very professional and courteous.
"But they had no explanation as to why it had taken so long for his interview to be conducted and frankly the evidence they presented to me was thinner than William Hague's hair."
He said the Mirror would continue to expose Mr Hewitt's "repeated and revolting attempts to cash in on Diana's memory".
"By doing so I firmly believe we are acting in the public interest," he said.
He also revealed that he had asked detectives whether there were any plans to investigate Mr Hewitt under the 1351 Act of Treason for committing adultery with the wife of a future monarch.
He said he was told no such investigation was underway.
'Proper function'
Michael Coleman, solicitor for James Hewitt, said: "Mr Hewitt is happy that the police force is carrying out its function responsibly and is properly investigating the crime at his home with a view to bringing those involved to justice.
"In view of the impending investigation, it would be inappropriate in my view to comment on Mr Morgan's press release until the conclusion of the criminal trial."