Mishra alleged that the man was associated with the Mohalla Clinic programme run under Health Minister Satyendar Jain.
Police have received a complaint from Mishra and are taking appropriate legal action, said DCP(North) Jatin Narwal.
Ruckus ensued at the protest site after the man, identified as Ankit Bhardwaj, allegedly attacked Mishra. Police officials and his aides caught hold of him.
In his complaint, Mishra had said that the man had arrived around 30 minutes before the incident happened.
"The guy came running, put his hands on my neck and said he would kill me. My aides caught hold of him and the police came and whisked him away," Mishra said.
Bhardwaj, while being whisked away by the police, told reporters that he attacked Mishra because "he has betrayed the party".
"Nobody has sent me here, I have come on my own. I am an AAP worker," Bhardwaj claimed.
The AAP has said Bharadwaj has no link with it and is working for the Bharatiya Janata Yuva Morcha (BJYM), the youth wing of the BJP.
Police said he pounced on Mishra when doctors came for Mishra's medical check-up. They, however, maintained that no attack has taken place.
"When Mishra's medical check-up was underway, he stood up and shouted, 'Why are you doing this?' He was whisked away by the police," said another officer.
A case has been registered for voluntarily causing hurt and criminal intimidation and police are trying to find out more details about Bhardwaj.
Police sources claimed that Mishra had asked police to be only stationed outside his residence and not near the venue of his hunger strike.
Mishra had recently made a startling allegation that he witnessed Delhi chief minister Arvind Kejriwal accepting Rs 2 crore in a dodgy transaction.
Mishra had yesterday alleged getting threat calls and launched a hunger strike this morning, demanding that AAP leaders disclose the details of funding for their foreign tours.
He claimed that the details of the foreign trips by AAP leaders would "reveal a lot" about alleged corruption by them.
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