According to TMZ, Edelman was walking around in Beverly Hills when he jumped on the hood of a car, causing damage to the vehicle.
Police were later flagged down and Edelman was arrested and cited for misdemeanor vandalism before being released.
Law enforcement sources tell Edelman it was apparent to them that he had been drinking.
It remains to be seen whether the L.A. County D.A. will file charges in the matter.
Edelman will reportedly undergo surgery for a separated AC joint in his left shoulder and to remove a loose body in his left knee this offseason.
Edelman, 33, is a former seventh-round pick of the Patriots back in 2009. He was entering the final year of his four-year, $17 million contract when the Patriots to a two-year extension worth up to $18 million last year.
Edelman stands to make a base salary of $3,300,000 for the 2020 season.
In 2019, Edelman appeared in all 16 games for the Patriots and caught 100 passes for 1,117 yards receiving and six touchdowns. He also rushed for 27 yards.