Maxwell was the only player in Major League Baseball this year to take a knee during the national anthem to protest racial injustice.
Scottsdale police said officers went to Maxwell's home Saturday night after getting a call about a person with a gun. Maxwell was booked on charges of aggravated assault with a deadly weapon and disorderly conduct.
Police said Maxwell was held in custody pending an initial appearance.
"We were disappointed to learn of the allegations," the A's said via statement on Sunday. "We take this situation and ongoing investigation seriously. We are gathering information from the proper authorities and do not have further comment at this time."
TMZ Sports first reported the arrest.
Maxwell, 26, hit .237 with 3 home runs and 22 RBIs in 76 games this season. He was projected to be Oakland's starting catcher next year.
The Associated Press contributed to this report.