Singh, who was remanded to judicial custody on August 10 after his arrest, is accused of creating enmity between different groups and inciting the youth.
Delhi High Court has earlier refused to grant any interim protection to Chaudhary, president of Hindu Rakshak Dal.
According to police, the FIR was filed against one Anwar Syed Faizullah Hashmi on the complaint of his neighbours.
In a video that surfaced online on Monday, Chaudhary is seen denying all allegations against him.
Jantar Mantar sloganeering case: HC issues notice to Delhi Police on Pinky Chaudhary's anticipatory bail plea
The trial court had stated that the country is not a Taliban state and the rule of law is the sacrosanct governing principle of our plural and multi-cultural society.
The arrest comes days after a Delhi Patiala House Court dismissed the bail plea of three accused in connection with sloganeering near Jantar Mantar.
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Police booked at least 10 youths who were seen raising the slogans in a video that went viral.
A Delhi court on Wednesday had granted bail to Upadhyay, who has denied any involvement in the alleged anti-Muslim sloganeering incident.
The prosecution opposed the bail on the grounds that release of the accused will create further law and order situation.
Shoukat Ali, a social activist, said, “If Muslims protest against CAA, they put us in jail and torture the innocents in custody.
Anti-Muslim slogans at Jantar Mantar: Court sends ex-BJP spokesperson Ashwini Upadhyay, 5 others to judicial custody
Duty Magistrate Tanvi Khurana sent the accused to judicial custody, considering that their bail applications were pending.
Anti-Muslim slogans at Jantar Mantar: Delhi Police detains former BJP spokesperson Ashwini Upadhyay, others
Hundreds of people had attended the protest organised by Bharat Jodo Aandolan at Jantar Mantar on Sunday.
For his part, Upadhyay said he was not responsible for the sloganeering. Sources said the Delhi Police chief asked officials handling the case to take strict action as per law.
FIR filed in connection with anti-Muslim slogans raised at BJP leader's event in Delhi's Jantar Mantar
Shipra Srivastava, media in-charge of Bharat Jodo Aandolan, said the protest was held under the leadership of advocate and former BJP spokesperson Ashwini Upadhyay.