Rana Gurmit Singh Sodhi, 67, is an MLA for the last four terms and is considered close to former Punjab chief minister Amarinder Singh.
The Sikh body filed a police complaint against her on Saturday for allegedly making seditious and derogatory remarks on social media.
Sikhs will never forgive Congress for felicitating 1984 riots culprits: Akali Dal leader Manjinder Sirsa
"Thirty-seven years after the anti-Sikh riots, the wounds have not healed as the culprits are still roaming free," Shiromani Akali Dal leader Manjinder Singh Sirsa tweeted in Hindi.
A controversy had erupted in late June over the construction of the Sikh shrine replica in the park built, following which it was removed.
“We are thankful to the Government of India for making sincere efforts for evacuating members of Sikh and Hindu community from Afghanistan after the collapse of Afghan Government.