The application is headed by the Directorate General of Information and Public Relations (DGIPR) which disseminates information to print and electronic media about government policies.
The trust, called Anulom, was started by one Atul Vaze with the "blessings" of Chief Minister Devendra Fadnavis, Chavan claimed in the Legislative Assembly.
Mr Chavan's allegation came on a day the Election Commission said that it will look into allegations of harnessing user data through mobile apps of political parties and personalities.
Recently, Mr Fadnavis felicitated active social media users called Mahamitras, who were chosen based on their activities on social media, their followers on Twitter, friends on Facebook, likes and contacts etc.
"These Mahamitras are being used to win over people's minds and their votes. All data collected goes to a private trust called 'Anulom', which was founded by Atul Vaze with the blessings of the chief minister," Mr Chavan said.
An app launched with government funds sends data to a private trust, which is a supporter of Mr Fadnavis, the Congress leader said, and sought to know if the BJP-led government had signed any MoU with the trust.
"What is being done is sociological micro targeting and weaponisation of data," Mr Chavan said.
"Data is being collected without consent of the user. This amounts to violation of privacy," he said.
Assembly Speaker Haribhau Bagde asked the government to check whether the state funds were used for data collection.
Mr Chavan later told reporters outside the House that the server of Anulom was based in Germany.
"Data of anyone who clicks on 'Mahamitra' app goes to the Anulom trust. Details of the social media app, photos and phone record details of the users go to this trust. This is just like how the NaMo app is used for political purpose," he alleged.
Refuting Mr Chavan's allegations, Minister of State for Home Ranjit Patil said no information had been shared with any private entity, especially Anulom.
"A total of 84,000 youths had participated in the Mahamitra initiative. The only information collected from them was mobile numbers and e-mails. No private information had been sought and nor was it given to any private party," Mr Patil told the Assembly.
The minister also rejected allegations of connections between Mahamitra and Anulom apps, claiming that the two were completely different.