Havertz and his wife were targets for online trolls after he missed in the penalty shootout defeat to FA Cup opponents Manchester United on Sunday.
Ahead of Wednesday's clash with Tottenham, Arteta snapped: "It's incredible honestly. We have to really do something about it, because accepting this I think has terrible consequences.
"It's so cynical, so dependent to an action.
"27 December at home, we win 1-0 Kai Havertz scores a goal, the whole stadium is singing the Waka Waka. Guys, what is the perspective?
"Everyone is responsible for the narrative. That is a really serious matter. It affects him, it affects me."
On Gabriel Jesus' knee injury suffered on Sunday, Arteta also stated: "Not looking good at all, but we need to review with the specialist and will have more information this afternoon."
On whether it was an ACL rupture, as has been reported this morning, he added: "I don't want to confirm anything until we have the final report this afternoon. We were every worried straight after the game and we are very worried today."
Asked about buying a replacement for Gabriel Jesus this month, Arteta insisted: "My answer doesn’t change. We are actively looking into the market to improve the squad. We always have been. It would be naïve not too. We are looking and we are trying, so let’s see what we can do.
"To recruit a player there are three parties who have to agree to that. The fact I love my players doesn’t mean we can’t think about improving. We do daily and when the market comes around we have to make sure we have the best resources and capacity to compete the way that we want to."