Arapahoe (Colo.) County sheriff Grayson Robinson told The Denver Post Lawson faces charges of physical harassment and criminal mischief in connection with an incident involving girlfriend Ashley Nicole Pettiford, who was also arrested.
Robinson said the pair broke each other's phone in the alleged dispute, with a mandatory restraining order issued after the arrests.
Lawson was freed on $1,000 bond Monday, the Post reported.
Nuggets General Manager Tim Connelly issued a statement saying the team was aware of the incident but otherwise didn't comment.
The point guard also ran afoul of the law last year when he was taken into custody for failing to appear on charges of driving under restraint and careless driving.