Urias, 22, was arrested Monday evening, booked and released on $20,000 bond several hours later, according to a Los Angeles Police Department arrest log.
He was arrested after authorities responded to reports of an incident in the car park of a Los Angeles shopping mall, with witnesses telling officers they saw a man later identified as Urias shove a woman.
"We learned about the alleged incident this morning and are in the process of gathering information," the Dodgers said in a statement Tuesday.
"As a result, we have no comment at this time regarding the incident. However, the very allegation of domestic violence must be taken seriously and addressed promptly, and we will cooperate fully with the authorities and Major League Baseball to ensure that happens in this case."
Major League Baseball commissioner Rob Manfred placed Urias on seven-day administrative leave, as outlined in the collective bargaining agreement. At the end of that period, the commissioner's office can extend the leave, reinstate him or suspend him.
Mexico's Urias is a rising star on the Dodgers' pitching staff. The left-hander made his Major League debut with the team when he was 19, building a 5-2 record in 15 starts in 2016.
A left shoulder injury in June 2017 sidelined him for more than a year, but he returned late last season and made relief appearances in the regular season and playoffs.
He was 2-2 in starts this year before being moved to the bullpen in a bid to limit his innings.