In a communication, the Home Ministry told the three states to beef up security and ensure that no violence takes place after the judgment tomorrow.
The three states were also told to deploy additional forces in sensitive places, the Home Ministry official said.
Rajasthan, Gujarat and Haryana have large number of followers of Asaram.
Prohibitory orders have already been issued in Jodhpur where the trial court will deliver its verdict in the Central Jail premises, as directed by the Rajasthan High Court.
"We have made all arrangements for the judgment day, DIG Jail Vikram Singh said.
The magistrate along with court staff, Asaram and the co-accused along with the defence and prosecution counsels will remain present in the courtroom in jail premises, he said.
Asaram is accused of raping a teenage girl from Shahajahanpur in Uttar Pradesh, who was studying at the godman's ashram at Chhindwara in Madhya Pradesh.
The victim had alleged that Asaram called her to his ashram in Manai area near Jodhpur and raped her on the night of August 15, 2013.
Security was also stepped up around the victim's house in Shahajahanpur.
"The security for the victim's family is continuously being monitored... Two more constables will stand guard outside her house in addition to the five policemen already deployed there, and a strict vigil is being maintained on all the visitors using CCTV cameras," Superintendent of Police K B Singh told PTI .
A vigil was also being kept on Asaram's ashram at Rudrapur, he said.
The Union Home Ministry's advisory was sent in view of the fact that large-scale violence was seen in Haryana, Punjab and Chandigarh after a special court pronounced its verdict in a rape case against Dera Sacha Sauda chief Gurmeet Ram Rahim last year.
Final arguments in the case had been completed by the special court for SC/ST cases on April 7 and the court had kept the order reserved to be pronounced on April 25.
Asaram was arrested in Indore and brought to Jodhpur on 1 September, 2013. He is under judicial custody since September 2, 2013.
The chargesheet against Asaram and four other co-accused Shiva, Shilpi, Sharad and Prakash had been filed by the police on November 6, 2013 under various sections of the POSCO Act, Juvenile Justice Act and IPC.
"We have imposed section 144 of CrPC in the city from April 21 and it would remain effective till April 30. Besides this, we have been keeping a sharp eye on Asaram's ashrams and checking all hotels and guest houses as well as the bus and railway stations, DCP (East) Aman Deep Singh said in Jodhpur.
We will also seal the jail on the day of judgment and would not allow anyone to get close to the jail premises, he said.
Asaram has unsuccessfully moved 12 bail applications, of which six were rejected by the trial court, three by the Rajasthan high court and three by the Supreme Court.