The 25-year-old midfielder has played every game this season but has picked up four bookings, leaving him just one away from a ban.
And Ward has warned the former Colchester man that his position could be under threat.
"He puts his own game on a knife edge and he's aware I'm not a fan of that," Ward told BBC Radio Bristol.
"He'll end up coming out of the team and someone like Seanan Clucas will come in and he may not get back in.
"He gets involved in unnecessary things. Tom Lockyer has established himself in there and shifted people out, so I'm sure Clucas can do it. John-Joe better beware."