The 49ers were informed Tuesday that Edwards would not miss any games because of the arrest.
Edwards, who signed a one-year contract with the team following the lockout, has had other run-ins with the law and was implicated in a bar fight in Birmingham, Michigan, just last month.
But the NFL said in a statement Tuesday that the fine was for the drunk driving arrest only.
"Any other matters will be addressed at the appropriate time," the league said.
Edwards was playing for the New York Jets when he was pulled over in Manhattan last year for having tinted car windows and failed a breathalyzer test. He pleaded guilty in July.
The 28-year-old has 326 catches for 5,142 yards and 39 touchdowns in seven NFL seasons for the Cleveland Browns and Jets.