Ethuro issued the writs on Thursday, one week after the former Education Minister was buried in his Mbooni home.
The issuance of the writs now clears the way for the Independent Electoral and Boundaries Commission to set the date for a by-election.
The commission now has the mandate to plan for the by-election to fill the vacancy within 90 days.
The law requires the Senate Speaker to issue writs within 21 days of the occurrence of any vacancy in the House.
Kilonzo was found dead close to three weeks ago at his Maanzoni ranch home.
The mystery surrounding the death of the Senator still lingers with results expected earliest in July.
Pathologists who carried out a post-mortem on the body of the late Kilonzo on April 30 said that they needed between eight to 10 weeks to make a conclusive finding on the cause of death.