Ibrahim, commonly known as Emmanuel, Rotich, was arrested last week in the coastal town of Mombasa after a dramatic late-night chase.
“The suspect will remain in police custody for 20 days to enable police to complete the investigations into the murder,” Iten chief magistrate Charles Kutwa said.
“He will also be taken for mental assessment.”
Tirop, 25, was found stabbed to death in their home in Iten, western Kenya, last Wednesday, a killing that shocked the nation and the world of athletics.
The double world championships bronze medallist was considered a rising star in Kenyan athletics. She came fourth in the 5,000 metres at the Tokyo Olympics this year and broke the world women-only record in the 10km last month.
Rotich, said by police to be aged about 41, had been expected to appear in court on Friday, but the hearing was postponed as officials decided where the case against him should be held.