The woman was attacked at about 23:20 BST on Saturday close to the junction of Tulip Street and Beza Road in the Hunslet area of the city.
West Yorkshire Police detained a 27-year-old man for questioning after his arrest on Sunday.
Detectives said the woman suffered a number of injuries in the attack and required medical treatment.
A man has been arrested on suspicion of raping a 54-year-old woman on a disused railway line in Leeds.