Selected by the San Jose Sharks in the seventh round (No. 201) of the 2007 NHL Draft, Braun was a late-round pick who has developed into a steady, stay-at-home defenseman.
After playing high school hockey in his home state of Minnesota, Braun played for Green Bay of the United States Hockey League before scoring 88 points (23 goals, 65 assists) in four seasons at the University of Massachusetts. Braun signed an entry-level contract with the Sharks on March 24, 2010, reporting to San Jose's American Hockey League affiliate in Worcester, Massachusetts. He made his pro debut a memorable one, with three assists against Hartford on April 7, 2010.