Lindsay, 20, told police she was driving with friends when they pulled into a hotel valet parking lane to dodge the photographers, the New York Post said Wednesday.
One shutterbug, identified as Giovanni Arnold, jumped on the hood of Lohan's vehicle, police said the actress told them.
Arnold's employer, INF Photo, told a different story. INF said Arnold was standing in front of Lohan's car when she put it in reverse, and then into drive, knocking him down.
The photographer was treated for minor injuries at a nearby hospital.
Lohan's father, Michael Lohan, was released Tuesday from a prison in western New York, where he served nearly two years for DUI and assault.
"I want the best for Lindsay," he told "Inside Edition" in an interview that aired Wednesday. "I'm just watching what's happening all around her. So imagine what's going on in her life."
While not faulting her for wanting to go to clubs, Lohan said he was proud of his daughter's decision to enter rehab.