The 26-year-old former first-round pick was examined by doctors after being hospitalized for his injuries, which are not believed to be career-threatening, the sources said.
While full details are not yet known, a source told ESPN.com that both hands were injured. Pierre-Paul suffered severe burns on the palm of one hand and the tips of three fingers, and one finger is being tested for nerve damage. He didn't lose any fingers, and doctors believe there will be no permanent damage or disfigurement of his hands.
Giants officials are in South Florida on Tuesday to visit Pierre-Paul in the hospital, sources told ESPN.
The Giants still were attempting to determine the extent of the injury and a prognosis as of Monday afternoon, according to the source. There is concern that Pierre-Paul's hand injury could force him to miss training camp and the start of the regular season, one team source told ESPN on Monday, but the Giants are still awaiting more medical answers.
The injuries stemming from the incident could affect Pierre-Paul's future with the Giants after the pass-rusher enjoyed one of his best seasons as a pro in 2014. The Giants used the franchise tag on the two-time Pro Bowler, but he has yet to sign the $14.8 million tender and is consequently not under contract.
The Giants would be OK with letting Pierre-Paul play out the 2015 season on the $14.8 million franchise number and be eligible for free agency again next year. Per NFL rules, the sides have until July 15 to negotiate a long-term deal. After that time, should he sign the tender offer, Pierre-Paul would be locked into a one-year contract for 2015.
Pierre-Paul started all 16 games, posted 12.5 sacks and forced three fumbles last season.
ESPN's Adam Schefter and Dan Graziano contributed to this report.