Geldimuradov, 73, was reportedly arrested on April 15 with his sons Muhammed, Abdullah, and Abdulhay.
His fourth son, Abdulmejid, was allegedly sentenced to three years in prison in February for "misusing urban water resources." No further explanation of Abdulmejid's crime was made public.
On June 20, Shiri Geldimuradov's body was delivered to his family.
Unconfirmed reports say he died in the Tejen prison some 200 kilometers east of the capital, Ashgabat.
It is not clear when Shiri Geldimuradov died.
Some reports have suggested that a day after his arrest in April, police found drugs and weapons at Geldimuradov's home in the Azatlyk district of Ashgabat. His close friends dismiss the discovery and say the operation against him was politically motivated.
The actions against the Geldimuradov family began after a deadly shoot-out in Ashgabat between members of an unidentified group and security forces in September 2007. His son, Atageldi, was reportedly arrested after the clashes and sentenced to 25 years in prison.
Turkmen authorities said at the time that the incident was a major operation by the government against drug traffickers.
Rights groups say Turkmenistan's undisclosed prison population includes scores of political prisoners despite President Gurbanguly Berdymukhammedov's efforts to paint himself as a liberal successor since he came to power after Saparmurat Niyazov's death in 2006.