Cornerstone Bar said the staff member contracted the virus "outside of their work environment", but they have made the decision to close as a precaution.
All staff members are being tested while management are taking a "pro-active approach to ensure that staff follow self-isolation and contact tracing protocols".
We take our responsibility within the community very seriously.
The pub's management said: "Although we are disappointed to close after all of our hard work ensuring that the correct systems and protocols were in place to open safely on the 29th of June, this is a small sacrifice to maintain the health and safety of our valued customers and staff. We take our responsibility within the community very seriously and customer safety is our top priority.
"All persons who need to be notified have been by the HSE Contact Tracing System, and we are taking all necessary steps to ensure a safe and speedy reopening. We appreciate your understanding at this difficult time and look forward to welcoming you all back as soon as it is safe to do so."
The news comes as the National Public Health Emergency Team (NPHET) met this morning to discuss whether pubs should be allowed to reopen on Monday, despite earlier plans for them to remain closed until at least September.
Pubs that do not serve food have been closed since mid-March with a number of planned reopening dates postponed due concerns regarding the rising rate of Covid-19 infections in the country.
Another pub in Dublin has announced it will close until further notice after a member of staff tested positive for Covid-19.
Slattery's in Dublin 4 says the HSE's Contact Tracing System has notified anyone affected and all employees are being tested.
A Government Covid-19 briefing will take place this evening with any updates on the pub situation likely to be revealed by NPHET.
