The Independent newspaper quoted government figures compiled between January 2003 and September 2005 that showed at least 1333 had been diagnosed with mental health problems while on duty.
Of these, 182 were found to be suffering from post-traumatic stress disorder; 601 had adjustment disorder or "combat stress"; 237 were diagnosed with depression; and 167 with other mental illnesses or substance misuse.
The daily claimed many Iraq veterans were not receiving adequate treatment for their conditions and said the issue raised questions about the level of healthcare for regular soldiers, reservists and part-time volunteers.
Group Captain Frank McManus, a senior military psychiatrist, was reported as saying that reservists and part-timers are most commonly affected.
"They are more vulnerable because in their normal working day and life they have no contact with the military, they are surrounded by people who cannot begin to understand what they went through in Iraq," he said.
It also quoted Charles Plumridge, of the Gulf War Veterans and Families' Association, as saying: "This situation is appalling. The [Ministry of Defence] should not be allowed to get away with it.
"I would not be at all surprised if the figures increase greatly."
The ministry was said to have told the newspaper it was aware of the problem "at the highest level" and was attempting to address the issue, particularly for reservists, by making the National Health Service more aware of the issue.
Britain currently has about 8000 services personnel stationed in the four southern Iraqi states. Since the beginning of military action to oust the Iraqi president Saddam Hussein in March 2003 101 have died.