Police Inspector H M Vyas of the Ahmedabad police's detection of crime branch said Das (46) shared the photo on his Twitter handle on May 8.
The photo shows Shah and Singhal at a public event five years ago, but Das tweeted it to mislead people and defame the minister's reputation, the official said.
Das has also been booked for allegedly insulting the national flag by posting on March 17 a morphed picture of a woman wearing a tricolour on his Facebook account, the official said.
A case has been registered against Das under IPC 469 (forgery) and section 67 of IT Act for the May 8 Twitter post, he said. Das has also been booked under sections of the Prevention of Insults to National Honour Act and IT Act for the March 17 Facebook post, the official added.
The ED on Wednesday arrested Jharkhand mining secretary Singhal in a case of money laundering involving alleged diversion of MGNREGA funds, and also seized over Rs 18 crore in cash from the house of a chartered accountant, allegedly linked to Singhal.
Das has directed the 2017 film Anaarkali of Aarah starring Swara Bhaskar, Sanjay Mishra and Pankaj Tripathi.
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