Never trust any answer that doesn't include a source. Cal Ripken's high his rookie year was 11 games.
I don't know if it's the most but I did find two players with streaks of 48 games in their rookie years.
Scott Podsednik from 5/27/2003 to 7/21/2003. http://www.baseball-reference.com/players/gl.cgi?n1=podsesc01&t=b&year=2003
Albert Pujols from 07/28/2001 to 09/22/2001. http://www.baseball-reference.com/players/gl.cgi?n1=pujolal01&t=b&year=2001
All time it's 84 by Ted Williams, Boston Red Sox - July 1 through September 27, 1949 http://en.wikipedia.org/wiki/List_of_Major_League_Baseball_individual_streaks