The Padres will announce a corresponding roster move on Friday or Saturday.
Smith was selected in the 14th round of the 2011 First-Year Player Draft out of the University of Oklahoma. He was 9-6 with a 3.85 ERA in 26 starts last season in the hitter-friendly California League.
This spring, he allowed 17 hits in 31 1/3 innings with six walks and 37 strikeouts. Opponents are hitting .155 against him. He has been clocked at 100 mph this season.
"One of the many things that stands out about Burch is he is a power pitcher with control," said Randy Smith, the Padres' vice president of player development and international scouting. "His stuff produces high strikeouts with low walks and hits. He has an explosive fastball, that will reach the upper 90s and will ride it up in the zone and sink it down in the zone. Burch will pitch with purpose and can get outs at the top and bottom of the zone."
Andrew Cashner was originally scheduled to start Saturday's game but he's been pushed back to Tuesday. He is fine, but the Padres wanted to break up him and Smith in the rotation as both are hard-throwing right-handers. This also allows the team to keep Cashner's innings down.
"He's got a big arm and a good, sound delivery," said Padres manager Bud Black about Smith. "He's thrown very well this season in Double-A. Our front office thinks very highly of this guy."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.