The San Francisco district attorney’s office declined to file charges Tuesday against Giants CEO Larry Baer after a physical altercation between the baseball executive and his wife was caught on video.

“After a careful review of the relevant evidence, including multiple videos, statements from several witnesses and the parties themselves, the evidence does not support filing criminal charges,” said Alex Bastian, a district attorney’s office spokesman.

Police and prosecutors were investigating the March 1 incident in which Baer caused his wife, Pam, to fall to the ground while struggling over a cell phone in an outdoor plaza in Hayes Valley. TMZ purchased publishing rights to a cell-phone video that shows Baer appearing to grab the phone from his wife’s hand while she sits in a chair. The two tumble over and Pam Baer is heard screaming, “Oh, my God, no, help!”

The video sparked strong reactions from Bay Area officials, residents and Giants fans alike. A group of Bay Area domestic violence advocates — and even San Francisco Mayor London Breed — weighed in on the incident this week, demanding Major League Baseball discipline Baer for his actions.

Even though Baer will not face criminal charges for the incident, he still may face discipline from the league, which has issued penalties to players who were accused but never charged with crimes.

The MLB suspended Chicago Cubs All-Star shortstop Addison Russell 40 games in September following a domestic-violence investigation for which he was never charged. Toronto Blue Jays closer Roberto Osuna was suspended for 75 games after being arrested for domestic violence in May. The criminal charges in that case were dropped.

The players are among nine suspended following MLB’s new strict policy on domestic violence that went into effect in 2015.

After hearing that the district attorney declined to file charges, Baer’s attorney, Cris Arguedas, said, “That is clearly the right decision based on the evidence, and we appreciate the thorough and professional investigation conducted by the police department and the district attorney.”

The short video of the incident posted to TMZ shows only a brief moment in a longer argument between Baer and his wife, witnesses at the scene told The Chronicle.

A security camera at a clothing store on Hayes Street captured the couple in a longer argument that ended with Pam Baer falling to the ground. An employee at the store confirmed that police had obtained the video and MLB officials were seeking to see the video, too.

The shop, Aether Apparel, declined to share the footage with The Chronicle. But a source familiar with the investigation said the extended footage, as well as witness statements, helped prosecutors in making their charging decision.

The video shows Baer and his wife in a verbal argument for roughly 25 minutes before things get physical, the source said. At one point, Baer is seen looking at his phone and showing it to his wife before she reaches for it, the source said.

Pam Baer unsuccessfully tries to take the phone a second time before eventually grabbing it from her husband, the source said. The video, according to the source, shows Larry Baer then trying to get the phone back, but Pam Baer puts her body between him and her right hand holding the phone.

Larry Baer goes for the phone a third time — this time while a nearby witness recorded the now-infamous video of them — and knocks his wife to the ground.

Attorneys for both spouses have called the incident an accident that happened following a dispute over a phone. The fall, they noted, happened because Pam Baer had an injured ankle.

Larry Baer issued his own statement in which he said he was “truly sorry for the pain that I have brought to my wife, children and to the organization.”

A source confirmed there was evidence Pam Baer had a preexisting injury and there was no evidence of an injury caused by the March 1 incident. The couple has no history of violence in their 30-year relationship.

Larry Baer is currently taking a leave of absence from the Giants. The team did not say how long he would step away from operations while the executive board manages day-to-day business.

Breed on Monday issued a statement calling on MLB to discipline Baer to “send a message that any and all acts of violence against women are unacceptable.

“While Mr. Baer has apologized and expressed remorse for his behavior, it does not excuse his actions and it does not erase what transpired. Mr. Baer’s actions were serious and wrong,” Breed said in the statement.

Evan Sernoffsky is a San Francisco Chronicle staff writer. Email: esernoffsky@sfchronicle.com Twitter: @EvanSernoffsky