An arrest log for the Santa Clara Police Department shows Miller, 27, was arrested last week at an undisclosed location.
The 49ers were looking into details, the team said Monday.
"The San Francisco 49ers organization is aware of the matter involving Bruce Miller," general manager Trent Baalke said in a statement. "We were disappointed to learn of these reports and will do our due diligence in collecting all relevant information."
Miller didn't immediately return a call for comment.
Miller spoke last fall of being newly engaged and buying a house after receiving a three-year contract extension in March 2014. The 49ers were committed to keeping a key member of their running game through the 2017 season.
Miller is a key run-blocker who cleared the way for Frank Gore's fourth consecutive 1,000-yard rushing season. He impressed the 49ers' brass when he converted from college defensive end at Central Florida to NFL fullback. He earned Conference USA defensive player of the year honors while becoming the school's all-time sacks leader with 36 before the 49ers selected him in the seventh round of the 2011 draft.
Miller also had 18 catches for 189 yards and two touchdowns last season for the 49ers, who went 8-8 and missed the playoffs for the first time in four years. Coach Jim Harbaugh departed for Michigan, and Jim Tomsula was promoted from defensive line coach to replace him.