In a statement, the club stated: "The latest round of PCR testing, which was carried out yesterday, has returned a positive result for one senior player and one academy player at Ulster Rugby. These players, who are currently asymptomatic, are now self-isolating in-line with public health protocols."
The North's Public Health Agency has since been contacted and the club are working with health officials to trace contacts of the two players.
Ulster Rugby is assisting two players who have tested positive for COVID-19.
For the full statement ⬇️https://t.co/rRaq0jxUat— Ulster Rugby (@UlsterRugby) October 7, 2020
Ulster Rugby medical director, Michael Webb said: “Following confirmation of two players testing positive, our priority continues to be the health and safety of our players and staff, so we have acted quickly with a number of measures, including standing down training from today, and asking those who have tested positive to self-isolate immediately.
“We will continue to work closely with the Public Health Agency and the IRFU to follow all of the necessary public health advice and assist with the contact tracing process as required, as well as provide support to the individuals involved.”
The Ulster senior men's team are due to face Ospreys this Saturday in Liberty Stadium in Wales.