The 24-year-old deleted his Twitter account last week after screen shots of comments he purportedly made appeared on the website of Miami New Times.
"Major League Baseball has completed its investigation into Jarred Cosart's possible connection to sports-related gambling," the commissioner's office said in a statement. "The investigation did not reveal any evidence to suggest that Cosart, who fully co-operated with the investigation, bet on baseball."
MLB said Cosart was fined for violating a rule that "prohibits players from placing bets with illegal bookmakers or agents for illegal book makers. This rule is strictly enforced and applies to gambling with illegal bookmakers on any sport or event."
The amount of the fine and the details of the rules violation were not announced.
Cosart said in a statement issued by the players' association that "I have never, nor would I ever, bet on" baseball.
"I'm sorry for any distractions this may have caused the Marlins, my teammates, coaches, and our incredible fans," Cosart said. "I'm glad to bring closure to this situation before opening day."
Marlins star Giancarlo Stanton said the issue hadn't caused a problem in the clubhouse.
"No, no distraction," Stanton said after homering in an exhibition game at the Marlins' Class A affiliate in Greensboro, North Carolina. "It's a good thing it was spring and not the season but even then, it turned out working out OK."
Redmond said he hadn't officially heard the decision. Told the outcome of investigation and the penalty, he said: "If that's the case, then that's good news."