In his application, Shah said he was a diabetic and required to undergo frequent medical tests and treatment.
Shah has also filed a discharge application in the court of special CBI judge BD Uptat which is likely to pass an order on June 16.
The court had on May 9 issued summonses to Shah and other accused in the case, which had been transferred from Gujarat.
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 is suspected to have links with the 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 eye-witness to the encounter, was killed by police at Chapri village in Banaskantha district of Gujarat in December 2006.
Shah, who was then minister of state for home, was allegedly involved in the conspiracy behind both the incidents.