Root, who finished the day on 111 not out, refused to divulge what Gabriel said when asked about the incident at the end of day's play, saying it should stay on the field.
He was named man-of-the-match on his home ground in Barbados after making an unbeaten 202 and taking two wickets in their 381-run win in the first test.
Root appeared to tell Gabriel "there's nothing wrong with being gay" while batting on day three in St Lucia, with the comments apparently picked up on television via the stump microphone. "I don't want anything said in the middle to ruin what's been a good Test series for him and his team".
Press Association reports Gabriel was spoken to by one of the on-field umpires about his language.
The Caribbean side lead the three-match rubber 2-0 following victories by 381 runs in Barbados and by 10 wickets in Antigua.
He added: "I wouldn't use the words so strong to say intimidate with pace but when you have pace, as someone who played the game as a fast bowler, it gives you more options of being able outfox the batters".
West Indies' interim coach, Richard Pybus, claimed he was unaware of the incident.
Meanwhile, Kirsty Clarke, the director of sport for the LGBT charity Stonewall, said Root's behaviour would help kick discrimination out of sport.
Pundits and fans have taken to social media to praise his forward-thinking actions, with former England captain Nasser Hussain describing Root as a role model.
West Indies vs England 3rd Test will be played at Daren Sammy National Cricket Stadium, Gros Islet, St Lucia from 19:30 IST.
"If Shannon Gabriel has really made a homophobic comment, [the] ICC should deal with it harshly", wrote cricket historian Abhishek Mukherjee.
"It feels fantastic. All the hard times I've had with injury, and the self-doubt, today I feel like an England", said Wood.
Joe Root's team had earlier slumped to 277 all out - having started the day 231-4 - but Wood and Moeen Ali (4-36) tore through the Windies and earned England a 123-run first-innings lead.