Ms Walker stayed with the distraught mother and her children.
Police arrested Roscoe Bradley Holyoake, 34, of Perth, Australia, on Friday.
Local media are reporting a 32-year-old mother was walking with her child in the Castro District of the city when a man allegedly tried to grab the boy.
A "tug-of-war over the child" allegedly then began between Holyoake and the mother who yelled: 'What are you doing?'
The mother chased down Holyoake and took back her son while bystanders detained the former Perth resident.
Mr Walker, a dentist, said he and other bystanders chased after Holyoake on foot.
She said she struggled with him and freed the boy from his grasp.
Holyoake, held on $US500,000 bond ($A697,000), will appear before a San Francisco Superior Court judge seeking bail on Thursday.
His attorney Steve Olmo told media outside court that Holyoake doesn't have a criminal record and was in San Francisco on business.
Mr Holyoake is a Perth DJ, known professionally as DJ Roski, who at one point was on the board of Pride WA.
'Overzealous police work, mistaken identity, wrong place wrong time, ' his lawyer said in reference to possible defences for his client. In addition to regular club night appearances and performances surrounding Sydney Mardi Gras, he has also volunteered for community radio station RTRFM.
He has worked as a DJ at Connections Nightclub in Perth and recently played at a wrap party for comedian Tim Minchin's new mini-series Upright.