His family members said an "intruder" fired at him on Friday morning.
Vikram, in his mid 30s, is the son of former Andhra Pradesh minister M Mukesh Goud.
He was found with bullet wounds in his body at his house in Film Nagar, an upmarket area of the city, under suspicious circumstances, the police said, adding that he was out of danger now.
"The incident occurred between 3 am and 3.30 am yesterday", said Deputy Commissioner of Police (West Zone) A Venkateshwar Rao.
Following a complaint from Vikram's wife, the police registered a case of attempt to murder under the Indian Penal Code (IPC) and added the relevant Arms Act sections to it.
Ten police teams have been formed to crack the case.
According to Hyderabad Police Commissioner M Mahendar Reddy, in her complaint, Vikram's wife Shipali M alleged that an "intruder" fired at her husband, following which she rushed him to a private hospital in their car.
Reddy said as per the sequence of events narrated by Shipali, the couple was getting ready to visit a place of worship and Vikram was waiting for her on the ground floor of their house.
"Suddenly, his wife heard gunshots and subsequently, found Vikram lying in a pool of blood on the ground", he added.
The DCP said that according to the doctors at the hospital, Vikram was out of danger now.
According to the hospital authorities, Vikram suffered bullet injuries on his arms, chest and spinal cord. One bullet had been removed, they added.
"He is in the ICU and his condition is stable", a source in the hospital said.
"The case is being investigated. We are scanning the CCTV footage obtained from the locality. We are reconstructing the crime scene. The victim is yet to reveal his version", said the police commissioner.
Mukesh Goud, a Congress leader, was a minister in the Y S Rajasekhara Reddy government in the united Andhra Pradesh.