"(Shah) is engaged in political work in New Delhi and therefore not able to come to court," read the exemption application filed by Shah's lawyer Robin Mogera.
Special Judge B H Loya later adjourned the case till July 17 after taking on record the exemption applications of Shah and some of the other accused.
Meanwhile the court is likely to hear Shah's discharge application on July 14.
Last time on June 20, Judge Loya's predecessor Judge J T Utpat had reprimanded the counsel of Shah for seeking exemption without assigning any reason to it.
"Every time you are giving this exemption application without assigning any reason," judge Utpat had said.
Judge Utpat was transferred to Pune on June 25.
The court had on May 9 issued summonses to Shah and other accused in the case, which had been transferred from Gujarat to Mumbai earlier this year.
The CBI had charge-sheeted Shah and 18 others, including several police officers, in the case last September.
According to CBI, gangster Sohrabuddin Sheikh, who was claimed to have links to Pakistan-based terror outfit Lashkar-e-Toiba, and his wife Kauser Bi were abducted by Gujarat's Anti-Terrorism Squad when they were on way from Hyderabad to Sangli in Maharashtra and killed in an alleged fake encounter near Gandhinagar in November 2005.
Tulsiram Prajapati, an eyewitness to the encounter, was killed by police at Chapri village in Banaskantha district of Gujarat in December 2006.
According to the CBI, Shah, who was then Minister of State for Home, was allegedly involved in the conspiracy behind both the incidents.