Jonathan Strobel suffered severe and "deep second-degree burns" on his right thigh and thumb when the phone exploded, palmbeachpost.com reported on Monday.
The lawsuit has asked for $15,000 in compensatory damages from Samsung.
Strobel later received an email from the company, requesting him to surrender Note 7.
"Samsung is a big corporation and they control the information that's put out. They obviously knew what was wrong (with the phone). Unfortunately for Strobel, it was too late for the mandatory recall, Strobel's lawyer was quoted as saying.
The US government has officially recalled the Samsung Galaxy Note 7 smartphones after dozens of reported cases in which batteries exploded or caught fire.
The US Consumer Product Safety Commission said in a recall notice that the move will include about one million units of Note 7 that were sold prior to September 15.
"Consumers should immediately stop using and power down the recalled Galaxy Note 7 devices purchased before September 15, 2016, " the notice said.
"Contact the wireless carrier, retail outlet or Samsung.com where you purchased your device to receive free of charge a new Galaxy Note 7 with a different battery, a refund or a new replacement device," it added.
Samsung has received 92 reports of the batteries overheating in the US, including 26 reports of burns and 55 reports of property damage, including fires in cars and a garage.
On September 8, a man's Jeep caught fire in St Petersburg as he charged the phone in the vehicle.
The US Federal Aviation Administration has also issued a warning, asking airplane passengers to not use or charge their Galaxy Note7 devices on planes.
Globally, the South Korean company has sold about 2.5 million units of Note 7 since the device was officially released in August.
Samsung said last week that it will launch media advertisements to apologise for the "discomfort and concern" caused due to the ongoing global recall of its Galaxy Note 7 smartphones.
The world's largest smartphone maker said it will soon run an advertisement in major media outlets to offer an apology for causing discomfort and concern to its customers due to faulty batteries in some Note 7 smartphones.
