Ulster have suspended all training at the club after one senior squad member and an academy player tested positive for Covid-19.
An Ulster statement said that five other players and a member of the support staff had been identified as close contacts of the two players.
Ulster said the two players are "currently asymptomatic" and are self-isolating in line with health rules.
Further contact tracing is ongoing after the tests took place on Tuesday.
Ulster Rugby's Medical Director, Michael Webb, said that the province had "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."
Further testing of players and staff is due to take place on Thursday.
In late August, Ulster training was stood down for one day after eight Academy players tested positive for Covid-19.
On Tuesday, Munster announced that one of their senior players had tested positive for Covid-19, with six further players in isolation having been identified as potential close contacts.
Ulster are next in action away to Welsh club Ospreys in the Pro14 on Saturday evening with Munster hosting Edinburgh on the same day.
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