Prozac is prescribed to more than 38m people world-wide, and has been one of the pharmaceutical industries biggest success stories of recent years.
However, tests using Lustral, a very similar medicine, suggests that the Prozac "family" of drugs, known as SSRIs, may have dangerous side-effects.
There has long been concerns that the drug is prescribed to patients who suffer only mild symptoms of depression, and who are not clinically ill.
The research was conducted by Dr David Healy, of the North Wales Department of Psychological Medicine.
He told BBC News Online: "There are risk with these pills and benefits.
"Doctors need to make sure that the people they give these pills to are going to benefit, and that taking the risk is worthwhile - I don't think that always happens."
Dr Healy found that two out of 20 healthy volunteers on Lustral became dangerously suicidal.
No such effect was found when the volunteers were put on an antidepressant of a different class called reboxetine.
One of the volunteers, a 30-year-old woman, had a nightmare about having her throat slit after one week on Lustral and by the end of a fortnight she felt suicidal.
SSRIs (selective serotonin reuptake inhibitors) like Prozac and Lustral act to modify levels of serotonin, an important brain chemical messenger generally thought to be associated with mood and feelings of pleasure.
Dr Healy has written to the Medicines Control Agency, which licences medicines in the UK, expressing concern about SSRIs.
He is also concerned that his research has uncovered a serious problem with the way drug trials in general are carried out.
Drug trials 'are flawed'
Drug trials, he says, are designed to test whether a drug can treat a condition, not to uncover evidence of side effects.
However, pharmaceutical companies argue that because no evidence of side effects has been uncovered, that proves their drugs are safe.
Dr Healy told BBC News Online: "This is a very worrying state of affairs.
"Potentially every person in the country is in a state of legal jeopardy where they are unable to obtain redress for problems caused by taking drugs."
Eli Lilly, the makers of Prozac, issued a response which said: "There is no scientific evidence that establishes a link between Prozac and violent or suicidal behaviour.
The statement quotes a 1991 finding from an advisory panel of the US Food and Drug Administration, which found 'there is no credible evidence of a causal link between the use of antidepressant drugs, including Prozac, and suicidality or violent behaviour".
It goes on: "Several studies suggest that Prozac actually reduces aggression and suicidal thoughts and behaviour."