He currently has three active International Cricket Council (ICC) demerit points to his name and a further offence in the Auckland test will activate an automatic one-match suspension.
"He'll have to be on best behaviour," Root said. "I'm sure there might be a bit of noise about that after what's happened (to Kagiso Rabada) – about demerit points and missing games."
South Africa paceman Rabada was banned for two matches after brushing against the shoulder of Steven Smith in the second test against Australia but was cleared by the ICC to play in the remainder of the series after winning an appeal.
Root said he wanted to be sure that Stokes would be available to play for a run of matches. The 26-year-old missed the Ashes tour of Australia and returned to action last month in the five-match one-day international series against New Zealand, which England won 3-2.
"You want to make sure, not just that (your players' behaviour) is sitting well with you, but they're able to be on the field for the next game and next series," the skipper added.
"For me, it's your team and you want to make sure you're heading up this team, and if it's portraying an image of something you don't like then I suppose that's on you."
Stokes' previous demerit points were picked up between October 2016 and September 2017 and will remain for a period of 24 months.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
