To reach the conclusion, Peter Schlegel of the Cornell Medical Center in New York City and team gave 35 healthy men doses of a third SSRI called paroxetine, sold as Seroxat or Paxil, over five weeks, and examined their sperm before treatment and four weeks in.
Apparently, the volunteers' sperm seemed healthy - amounts of sperm and semen and the shape and motility of sperm - were all normal.
However, when the team looked at DNA fragmentation in the sperm, using the TUNEL method, a disturbing picture emerged.
The researchers found that on average, the proportion of sperm cells with fragmented DNA rose from 13.8 per cent before taking paroxetine to 30.3 per cent after just four weeks.
Similar levels of sperm DNA damage have been linked to problems with embryo viability.
The researchers are concerned that some men currently taking SSRIs may be suffering damage to their fertility.
The team will present its results in November at a meeting of the American Society for Reproductive Medicine in San Francisco, California.
"This study was not conducted by GSK, and therefore we are currently reviewing the investigators' findings. We take seriously our responsibility to ensure our medicines are used safely," New Scientist quoted Janet Morgan, a spokeswoman for GlaxoSmithKline, which sells paroxetine, as saying.