The 25-year-old man was detained last night and was today in custody, said West Yorkshire Police.
A 16-year-old youth arrested on Sunday as part of the investigation has been released without charge.
The 39-year-old victim was attacked while out jogging at about 6am last Wednesday on the towpath of the stretch of the Leeds and Liverpool Canal that runs between the A58 in the city centre and Viaduct Road in Kirkstall.
Detectives want to hear from people who were in the area at the time of the incident, particularly a number of cyclists who were filmed on CCTV.
Anyone with information is asked to contact West Yorkshire Police’s Homicide and Major Enquiry Team via the force’s 101 phone number or Crimestoppers anonymously on 0800 555 111.