It was during one of the Instagram live sessions with Indian vice-captain Rohit Sharma that Singh made the offensive comment about Chahal, while talking about his regular social media posts.
Singh (39) had apologised for the remarks, saying he "unintentionally" hurt public sentiments.
"An FIR has been filed against Yuvraj Singh based on a complaint by lawyer Rajat Kalsan at the Hansi Police Station," Hansi Superintendent of Police, Nikita Gahlaut said on Monday.
She said the case was lodged on Sunday under various provisions of IPC and the SC/ST (Prevention of Atrocities) Act.
Kalsan had filed the police complaint last year.
Police said the FIR has been lodged under IPC sections 153 (giving provocation with intent to cause riot), 153 A (promoting enmity between different groups on grounds of religion, race, place of birth, residence, language, etc.) and under the SC/ST (Prevention of Atrocities), Act.
Kalsan had alleged that Singh's comment had hurt the sentiments of the Dalit community, stating that a large number of people had watched the video on social media.
The lawyer had also complained to Haryana Home Minister Anil Vij, who had ordered the Haryana Director General of Police to take action in the matter.
Kalsan had also filed a petition in the special court established under the SC/ST Act in Hisar. The court had summoned the status report of the case from Hansi police.
Expressing regret over the comments, the former India cricketer had tweeted, "I understand that while I was having a conversation with my friends, I was misunderstood, which was unwarranted. However, as a responsible Indian I want to say that if I have unintentionally hurt anybody's sentiments or feelings, I would like to express regret for the same."
— Yuvraj Singh (@YUVSTRONG12) June 5, 2020
Known for his pivotal role in winning World Cups for India twice--2007 and 2011, the 39-year-old called curtains on his cricket career in June 2019.