USA Today Sports reported Wednesday that the fine will be for one week's pay on his base salary of $495,000, which amounts to $29,117.
Randle was charged with a misdemeanor Class B theft of $50 to $500, according to police. He was released on writ bond at 1:20 a.m. Tuesday.
Frisco Police Lt. Jason Jenkins said Randle is accused of attempting to steal underwear and cologne from Dillard's in Stonebriar Centre Mall.
Randle met with Garrett on Tuesday and addressed his teammates on Wednesday morning.
"I can't just go like nothing happen, I had to address the issue and we're trying to move forward from it," Randle told reporters after practice. "This is not a distraction from the team, we're just trying to get ready and keep winning like we been doing.
"We have to play our rival team, the Giants, and that's what we're focusing on."
Garrett said Randle will play in Sunday's game against New York.
"He took full responsibility for it," Garrett said. "There were a lot of circumstances that were surrounding the situation, but there are no excuses, no explanations for this. He took full responsibility, and he made a really poor decision. He recognizes that.
"This is the poorest decision he ever made in his life and, again, there are consequences to those decisions, and we made that abundantly clear with him. There are public consequences, and there are certainly consequences on this football team. He understands that, and he's going to feel that and we're going to move forward."
The arrest report states that store security officers, watching via the closed-circuit surveillance system, observed Randle purchase an item at the perfume counter before walking to the underwear section and concealing merchandise in his Dillard's bag. He then exited the store before being stopped by security in the parking lot.
The store security officers recovered from Randle a two-pack of black Polo underwear valued at $39.50 and an almost full "tester" bottle of Gucci Guilty Black cologne valued at $84.
Randle has been praised this season by Cowboys coaches. He's second on the team with 113 rushing yards and has three special-teams tackles, including one to stop Percy Harvin on a kickoff return during last week's victory at Seattle.