Sheku Bayoh, 31, died on Sunday after being detained by police in connection with an incident in Kirkcaldy.
The Police Investigations and Review Commissioner (Pirc) has begun looking into the circumstances surrounding his death, which followed an incident in the town.
Police Scotland refused to comment on the officer’s condition or injuries, but said she had not been stabbed.
It has been reported that she sustained her injuries as she attempted to arrest Mr Bayoh.
Fife divisional commander Chief Superintendent Garry McEwan said: “This is a tragic set of circumstances and my condolences go to the man’s family.
“The investigation of deaths in Scotland is the responsibility of Crown Office and Procurator Fiscal Service, who have instructed the Police Investigations and Review Commissioner to lead on this inquiry.”
The Pirc, an independent body which investigates serious police incidents, said it would report its findings to the Crown Office in due course.
A spokeswoman said: “The Crown Office and Procurator Fiscal Service (COPFS) has directed the Police Investigations and Review Commissioner to carry out an independent investigation into the circumstances surrounding the death of 31-year-old Sheku Ahmed Tejan Bayoh in Kirkcaldy on Sunday 3 May.
“He had been detained by police shortly before his death. A report on the Pirc’s findings will be submitted to the COPFS in due course.
“As this is a live investigation it would be inappropriate to comment further at this time.”
Mr Bayoh, who was known as Shek to his friends, is believed to have a partner and young son
A friend posted a picture of Mr Bayoh on Instagram with the message: “RIP Soldier Shek. You were a great friend and honestly a gift to anyone that knew you. I will never forget the things we got up to. The world has lost a great person.”