Obare was represented by lawyers Titus Munene Kinyua and Ojijo Kepher.
The case will be mentioned on August 21, while the hearing has been set for November 2.
Obare has been told to refrain from talking about the case.
Obare was arrested on Thursday in Kisumu and taken to DCI headquarters in Nairobi for questioning.
He had published passport details of Githinji, with a visa alleging she had travelled to Dubai.
At the time, international flights had been suspended.
Obare linked Githinji's travel to that of two legislators - Mombasa Governor Hassan Joho and Suna East MP Junet Mohamed - who had also travelled to Dubai to visit ODM leader Raila Odinga.
Raila had travelled to Dubai to undergo surgery on his back.