The Kenyan police say Emmanuel Rotich is of interest to their probe into Tirop's death by stabbing and will be charged at the end of the investigations.
At the time of her murder 25-year old Tirop lived in Iten town in western Kenya, reputed as a training hub for local athletes.
She set a new women's world record in the 10km road race in September.
The Kenyan police say Mr Rotich is the prime suspect in her murder and is currently detained after he was arrested in Changamwe, Mombasa County.
According to police accounts, he was intercepted as he tried to leave Kenya in an attempt to apparently escape and "evade justice".
A Kenyan police tweet suggested that Rotich's getaway vehicle had ploughed into a lorry as he unsuccessfully made a dash for it.
Following news of the murder, Athletics Kenya said it was suspending all athletics activities for two weeks as the sporting fraternity mourns Tirop.
She won bronze in the 5, 000m of the junior world championship in 2012 and 2014.
As a senior athlete, she won the World Cross Country championships in 2015.
She was fourth in the 5,000m final at the Tokyo Olympics.