The outspoken British singer, a longtime lover of Rome who has returned to the Italian capital to record an album, said the officer unlocked his gun and "screamed into my face" as a crowd of more than 100 people watched.
Morrissey's nephew Sam Esty Rayner, a photographer who often takes footage of the singer, posted a picture of the officer and wrote his motorbike's license plate number on Facebook.
"The Police Officer pictured below terrorized Morrissey for 35 minutes demanding 'papers'. Morrissey had no papers," Rayner wrote.
Morrissey in a statement accused the officer of a "deliberate act of terror" and said he had not broken any law.
"I believe he recognized me and wanted to frighten me. I did not back down even though I believed he was about to shoot me," Morrissey said.
"I urge people to beware of this dangerously aggressive Officer. He might kill you," he said.
Morrissey has frequently criticized the police both in his music and off-stage. In 2015, he said he was "sexually assaulted" by an officer at San Francisco International Airport who touched him during a security check.
The singer, who first found fame as the frontman of The Smiths in the 1980s, has won a fanatical fan base with his elegant and sardonic lyricism that often takes up life's disappointments.
Morrissey is a staunch opponent of the British monarchy and campaigner for animal rights, with the singer refusing to play in venues while meat is served.