Barton, who batted .226 with nine homers, 47 RBIs and a .327 on-base percentage over 140 games, had surgery to repair a labral tear in his right hip. Smith, who went 7-16 with a 4.16 ERA in 32 starts, had what the team called "loose bodies" removed from his pitching elbow.
Assistant general manager David Forst said Barton's injury started to surface late in the season, when he also dealt with minor groin issues, but Forst but said the hip was "not a factor at all" in Barton's performance.
"He swung the bat in the last month as well he he did all year," Forst said of Barton, who finished the year by going 8-for-14 with four doubles.
Smith's injury, Forst said, happened at home recently.
"Apparently, he was going to sit down and braced himself on a chair when he felt a pop," Forst explained. "The doctors speculated that maybe he had a bone spur that became dislodged, so they went in and cleaned some things out.
"It was kind of a freak thing."
Smith is expected to be out of action for six to eight weeks. Barton will be on crutches for six weeks, and the A's are hopeful that he'll be fully recovered in three months.
Mychael Urban is a national writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.