The two sides played out a 0-0 draw in Turkey, with the second leg in England on Thursday.
However, the Turkish club declined to sell tickets to their supporters.
And Burnley have decided to close the away end for the game, which means there will only be home supporters in the stadium.
A Burnley Football Club spokesman said: "Due to Istanbul Basaksehir's decision not to sell tickets to any of their supporters, the visiting section at Turf Moor will be closed for Thursday night's Europa League tie.
"No tickets will therefore be sold to any visiting fans for any area of the ground.
"And to comply with UEFA regulations regarding segregation, any supporter buying tickets for the home section must have a Clarets number as a member with a previous buying history at the club.
"Security and safety of all supporters attending Turf Moor is paramount at all times.
"Burnley Football Club apologises for any inconvenience this may cause and thanks you for your support."