Bourn has not played since Saturday, when he jammed his thumb sliding into second base for a double in the Braves' 8-2 victory over the Phillies.
Gonzalez said Bourn used a thumb guard when he took some swings in the indoor batting cages Wednesday, but he still felt discomfort.
"He's progressing well," Gonzalez said. "I said, 'Let's just take another day. Hopefully today will get you over the hump and we'll get you [back] tomorrow.'"
With the Braves having already clinched a spot in the playoffs, they are being cautious with Bourn -- just as they were with shortstop Andrelton Simmons and his jammed shoulder last week.
Jose Constanza takes Bourn's leadoff spot in the lineup and in center field against Josh Johnson and the Marlins. It marked Constanza's first game in center field this season. He played four games there last season.
Gonzalez said instead of starting Reed Johnson, a right-handed hitter, against Johnson, a right-hander, or sliding right fielder Jason Heyward into center field as they did twice earlier in the season when Bourn needed a day off, he opted for Constanza.
"Heyward, for me, is the best right fielder in the Major Leagues," Gonzalez said. "You put him in center field, he becomes, maybe, average, and now you put Constanza in right field. He is, maybe, below average in right field. So now you kind of weaken yourself at two positions."