The team announced both moves in a press release on Tuesday.
Barney, 28, batted .230 with two home runs and 16 RBI over 72 games with the Cubs this season.
A fourth-round pick out of Oregon State in 2007, Barney won the National League's Gold Glove award at second base in 2012 and has posted a .244 average over 542 career Major League games.
Bonifacio, who was dealing with a rib injury, has batted .261 with one home run, 16 RBI and 13 stolen bases in 61 games this season.
The Cubs opened Tuesday in last place in the NL Central at 40-57.
- Chris Johnson