Khan, 70, has suggested that there could be two people who shot at him at an anti-government rally in the eastern city of Wazirabad last Thursday.
The former cricket star, who has been pressing for early elections since being ousted as premier after losing a Parliament vote in April, is recovering from leg wounds at his home in the city of Lahore.
Police identified the suspect as Mohammad Naveed, a man in his 30s.
A copy of the police report, which was seen by Reuters, said a man in the crowd near Khan had taken out a pistol and started shooting, wounding Khan and 10 other people, one of whom later died.
Police said the suspected shooter was arrested after Khan supporter Ibtesam Hasan overpowered him and threw off his aim.
Regional police chief Akhtar Abbas told Reuters that a criminal investigation had been launched after the registration of a formal case.
Interior Minister Rana Sanaullah said on Tuesday the suspect was self-motivated.
“The things we got from his cell phone showed that he was fully motivated, fully committed,” he told a news conference.
Reuters journalists last Friday visited the district of Wazirabad where the suspect lived in a dingy house with his widowed mother, wife and two sons — the youngest just 2 weeks old.
Police confirmed to Reuters on Tuesday this was the same man as the suspect Mohammad Naveed named in the case.
Neighbors said he had this year returned from Saudi Arabia, where he had worked as a plumber for several years.
They described him as a quiet person and said his connection with the attack came as a surprise, although he had shown some signs of religiosity since his return to Pakistan.
“I knew him since his childhood, he had no bad habits, his act just shocked us,” said neighbor Mohammad Saddiq, adding the man lately had preached to him about saying his prayers.
He attended a neighborhood mosque and had recently objected to a music event at a nearby school, asking to ensure the music was not played at prayer time.
Khan said on Twitter on Tuesday that the police case was “farcical.”
He has accused Prime Minister Shehbaz Sharif, Interior Minister Rana Sanaullah and intelligence official Major-General Faisal Nasser of planning to assassinate him. The government and military have denied this.
Khan launched what is known as a long-march protest rally from Lahore to the capital on Oct. 28, which his party said will resume on Thursday at the same place where he was attacked.
Khan supporters blocked roads near the capital, Islamabad, on Tuesday, disrupting traffic and forcing schools to close.