“We know who he is and his chances of escaping are very bad,” Tuncel Aldemir, head of the Istanbul police's homicide department, told Swedish tabloid Aftonbladet on Monday.
The woman, who was from the Östergötland region in central Sweden, was reportedly at the night club in Turkey to attend a bridal shower.
She was shot dead when she stepped outside for a breath of fresh air.
“She got caught up in a shootout and died from her injuries,” Lilian Willix Schwirtz at the Foreign Ministry's press office told Swedish newswire TT.
The woman's relatives have been informed of her death.