Kirkstall Bridge Inn made the announcement on Friday afternoon.
The statement said the pub would be closed until Monday June 28 due to a "cascade of venues whose teams" are "being told to isolate by test and trace".
It continued: "Unfortunately, we have been affected by this and as a result, we've made the decision to close The Bridge until Monday 28th.
"Regarding bookings, most have already been contacted and relocated.
"We are continuing to reach out to those who were hoping to visit this weekend.
"To staff all our venues early next week, we will be operating with reduced opening hours.
"At The Bridge from Monday to Thursday, we will be accepting walk-ins exclusively and it will be outside seating only.
"While the kitchen will be closed, we will have Spuds & Bros serving poutine through till 8pm, Monday to Thursday.
"Bookings are still being accepted at the Taproom and The Cardigan Arms."
The pub said as it stands, normal service will resume on Friday July 2.
The statement continued: "We’ve always strived to keep our venues open, serving their communities, and adhering to the strict Covid safety measures throughout the past year and a half.
"The safety of our customers and our team comes above all else.
"Therefore, we’ve been working diligently alongside Public Health England, getting our venue deep cleaned and ready to welcome customers back as soon as possible.
"We would also remind and encourage people to keep wearing their masks whenever they are on their feet in our venues (regardless of how many vaccines they may have had)."
Staff at the pub thanked customers for their "patience and goodwill as we do our best to respond during this ever-changing situation".
For full opening times, visit Kirkstall Bridge Inn Instagram page.