The alleged racist gesture took place Sunday at AT&T Park after Jones hit a three-run home run against the San Francisco Giants, USA Today reported Monday.
"I want to thank whatever [expletive] threw that banana towards my direction in the CF last inning. Way to show ur class u [expletive]," he wrote on Twitter.
There was no video footage of the incident, USA Today said.
Throwing bananas is a racist gesture against black athletes that is especially rampant in European soccer, particularly in Italy, the newspaper said. Since one can't purchase bananas at a ballpark, the fan would have had to come armed with the fruit, presumably with the intention of throwing it at an athlete.