Ulster have identified "a number of Covid-19 cases" within their academy squad.
Senior and academy training has been stood down, while the province has said that anyone who was potentially exposed to the coronavirus is already in self-isolation. That includes one member of the senior squad.
The Public Health Authority has been contacted and the contact tracing process has started, Ulster added.
The senior squad underwent routine testing on Wednesday, with results due to be released today.
"Following confirmation of multiple academy players testing positive for Covid-19, we are closely following public health advice in line with the IRFU's return-to-play protocols," said Ulster's medical director Michael Webb.
"As a result, we have taken a number of precautionary measures as we await the results of further testing. We are supporting the individuals involved and all will continue to be medically monitored.
"Our top priority is to ensure the health and safety of our players and staff, and we will continue to work closely with both the IRFU and PHA as we look to make a safe and measured return to rugby."
Ulster were beaten by Connacht in the Pro14 on Sunday at the Aviva Stadium. They had been due to face Leinster at the same venue this on Saturday evening.