The cinema, located in The Capitol Centre on London Way, has undergone a "precautionary deep cleaning" as a result of the positive test and will remain open to the public.
A spokesman for Vue said an investigation, including a review of CCTV footage, has confirmed all safety measures were properly followed on site, PPE was used at all times and social distancing was observed.
"The safety of our staff and customers remains our top priority and precautionary deep cleaning has been carried out. We will continue to follow government safety guidelines to the letter," they added.
The news comes after Vue announced four of its cinemas in Lancashire, along with a string of other venues, will shut for three days a week in an effort to reduce costs following delays in the release of a string of blockbusters.
The cinema chain has now reduced its opening hours at 21 of its 87 UK sites, keeping them shut on Tuesdays, Wednesdays and Thursdays.
The venues in Lancashire affected by the move include, Accrington, Blackburn, Cleveleys and Lancaster - Preston will remain open as usual.
This comes after rival chain Cineworld announced it will temporarily close 127 Cineworld and Picturehouse sites in the UK.
Tim Richards, chief executive of Vue, previously said cinema chains were dealt a "body blow" by the delay to the next James Bond film, No Time To Die, until April next year (2021).
Marvel film Black Widow, sci-fi blockbuster Dune and Jurassic World: Dominion are also among the high-profile titles that have seen release delays as a result of the global pandemic.
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