The incident occurred shortly after midnight Wednesday in California, when Cabrera was stopped by Border Patrol.
The California Highway Patrol said the shortstop was cited and released into the custody of his mother-in-law.
“We were made aware of an incident involving Everth Cabrera this week, and we take this matter very seriously," the Padres said in a statement.
The 27-year-old is currently on the disabled list with a hamstring injury. He has played 90 games for the Padres in 2014, hitting .232 with three home runs, 20 RBI and 18 stolen bases.
Cabrera was one of 13 players suspended by MLB in August 2013 for taking performance enhancing drugs in connection with Biogenesis. He served a 50-game suspension.
- Molly Geary