A 17-year-old Dortmund supporter is believed to have made a complaint to police, accusing Lewandowski of punching him on the forehead on Thursday.
Reports have claimed that the fan made an offensive gesture to Lewandowski as the Poland international drove past in his car near his home.
According to Eurosport, Lewandowski has responded by writing on his Facebook page: "I want to clearly state that I never used violence against people who violated my private sphere. I have no intention of teaching teenagers how to behave but I will not allow for my family and myself to be offended."
The 25-year-old has sparked anger among a number of Dortmund fans by agreeing to join Bundesliga rivals Bayern Munich in the summer.