The lawmaker said a similar attack was attempted on his family house in Kaduna, but was unsuccessful due to the quick intervention of vigilant residents.
Gunmen had on Saturday, December 3, stormed the Senator's office, but the quick arrival of the police was said to have prevented the building from being set ablaze.
In a post on his Facebook page, Sani said el-Rufai should be held responsible for the attack.
The lawmaker said the attackers, who were heavily armed, raided and vandalised properties at his constituency office located at Stadium Roundabout by Constitution Road, Kaduna.
According to him, the thugs unleashed terror on his social media team who were meeting in the office at the time.
He said: "We have the lead and the information that thugs were fully recruited and paid by political appointees of Governor Nasiru Elrufai. We have the names of the political appointees and we have the names of those they are funding. Right now their details are given to the DSS and the police for investigation."
The Senator said an attempt was made to burn down his Family house in Alkalawa Road, Tudun Wada Kaduna, two days ago.
Sani said the attack was foiled by vigilant residents and neighbours, which led to the brief deployment of policemen in the area.
He added: "I wish to state it categorically clear that I hold Governor Nasiru Elrufai personally responsible for whatever happens to me or any of my family members or supporters. After the use of financial inducement on APC Excos in the state to silence Shehu Sani in the name of suspension, which never worked, they have now taken the road of violence.
"The Governor of the state or his desperate political appointees should know that we can never ever be silenced, coward or intimidated. I call on my supporters never to take the road of violence or retaliation.
"We are men of ideas, of ideals and of peace.Those who take to the road of violence have no place in a democratic society."
A faction of the APC loyal to the Governor had recently announced the indefinite suspension of Sani from the party.