Santa Clara police Lt. Kurt Clarke tells the San Francisco Chronicle that McDonald was taken into custody at 7 a.m. Monday on suspicion of domestic violence and child endangerment.
Clarke didn't immediately return calls or an email from The Associated Press.
The Bears did not respond to a message seeking comment Monday.
Chicago signed McDonald to a one-year contract in late March knowing it was a gamble given his history of legal issues.
Chairman George McCaskey even acknowledged at the time that he initially told new general manager Ryan Pace not to go after him.
But McCaskey came away impressed from a face-to-face conversation that he described as "very candid, very forthright" and "difficult" after McDonald paid his way to Chicago.
In December, the 49ers released the 30-year-old, citing a "pattern of poor decision-making."
In letting him go late in the season, 49ers general manager Trent Baalke said, "Ray's demonstrated a pattern of poor decision-making that has led to multiple distractions to this organization and this football team that really can no longer be tolerated."
His release from the team came just a month after the Santa Clara County district attorney's office announced it had declined to file charges against McDonald in a separate domestic violence investigation stemming from an arrest on Aug. 31 while celebrating his 30th birthday at his Northern California home.
Prosecutors cited conflicting versions of what happened, a lack of verifiable eyewitnesses and a lack of cooperation by the alleged victim, McDonald's fiancee, in explaining their decision not to pursue charges in the domestic violence investigation.
But his trouble continued.
In March, McDonald filed a defamation lawsuit against a woman who had accused him of rape.
McDonald says security camera footage will show a consensual sexual encounter occurred in his hot tub.
Police say the woman doesn't recall any sexual encounters and reported blacking out after drinking alcohol and falling at McDonald's home.
She said she went to police after waking up naked next to McDonald. The Santa Clara County district attorney is considering whether to file criminal charges.
McDonald had been signed by the 49ers through the 2015 season. He had three sacks in 14 games last year.
McDonald had 19 1/2 sacks in eight seasons with the 49ers.