The incident was caught on video and published on TMZ Sports. In the video, Larry Baer appears to knock his wife to the ground in an attempt to grab a cellphone.
His wife, Pam Baer, screamed "Oh, my God, no!" as she was knocked over while sitting in a chair. The video shows Baer walking away with the cellphone and saying "Pam, stop."
Larry Baer spoke with the San Francisco Chronicle about the incident and told reporters he apologized to his wife.
"My wife and I had an unfortunate public argument related to a family member, and she had an injured foot and she fell off her chair in the course of the argument," he said. "The matter is resolved. It was a squabble over a cellphone. Obviously, it's embarrassing."
The couple later released a statement through the Giants organization, saying: "Regrettably today we had a heated argument in public over a family matter. We are deeply embarrassed by the situation and have resolved the issue."
The MLB acknowledged the incident and released a statement.
"Major League Baseball is aware of the incident and, just like any other situation like this, will immediately begin to gather the facts," the statement said. "We will have no further comment until this process is completed."
Larry Baer was a member of the ownership group that purchased the Giants in 1992 to keep the franchise in the Bay Area. San Francisco won the World Series in 2010, 2012 and 2014. Larry Baer became the organization's CEO on Jan. 1, 2012.
The couple have been married for almost three decades and have four children together.