Bradley, who became the first player to win a major using a belly putter at last year's PGA Championship, was accused of being a cheater by a fan as he played the final hole in Saturday's third round at Sherwood Country Club.
"This is a deplorable incident, and there is no place in our game for this kind of behaviour," the USGA said in a statement before Sunday's final round of the 18-player event hosted by Tiger Woods.
"As we noted when announcing proposed Rule 14-1b, it has been and remains entirely within the rules of golf for players to anchor the club while making a stroke.
"There should not be a shred of criticism of such players or any qualification or doubt about their achievements, and we think that it is inappropriate even to suggest anything to the contrary."
Bradley has been among several players under the spotlight since Wednesday's proposal by golf's rulemakers to ban putters being anchored to a player's chest, stomach or chin.
The ban would not come into effect until 2016 at the earliest, and for the next three months both the Royal and Ancient (R&A) and the USGA will be seeking feedback on the proposal.
"We are sorry that Keegan had to experience this unfounded criticism from an obviously uneducated spectator," the USGA said.
"Instead, Keegan and other PGA Tour professionals should be commended for their maturity and grace in managing through a proposed change to the rules of golf."
Bradley, a three-times winner on the PGA Tour, said he had never been heckled before until Saturday's incident.
"I've never heard anything negative," the 26-year-old said. "But I look forward to hopefully making everything (in Sunday's final round) with that belly putter and hopefully it (the criticism) will get a little louder."
Asked if he had responded to the fan on the 18th hole, Bradley replied: "No. You know, that's unfortunate. It's very disrespectful.
"But it's fine with me. I've got to try to look at it as motivation to help me try to win this tournament."