Ahead of their trip for Saturday's early kickoff, Arteta addressed Havertz's hamstring injury suffered on the final day of training for their Dubai warm weather camp.
It means attackers Havertz, Gabriel Jesus, Bukayo Saka and Gabriel Martinelli are all sidelined.
Arteta said, "We were having a great camp in Dubai, recharging , training, connecting with nature and different environment. Then the injury happened in unexpected way, it's a big blow because of injuries we have.
"He was going to stop a shot, he stretched the leg and he done his hamstring.
"Fortunately we have been through a lot this season, it's the challenge I have. We love it. Let's see what the team is made of.
"Any team in this league losses four players in frontline like that and I know what the answer will be."
Asked about options to cover the attacking absences, Arteta said of teenager Ethan Nwaneri: "It's a question of when, he has the right qualities, to play out wide or centrally. We must adapt to the strengths of our players."
Arsenal allowed the winter market to close without signing a new striker, including Ollie Watkins, who was offered by Aston Villa for a price of £60m.
Pushed if he now regrets not acting, Arteta said: "We always knew that we were an injury or two away. But when you try everything you can, we have to deal with it."
However, asked about the free agency market, he refused to rule anything out: "We will explore every possible situation."
The Gunners manager says they could turn to Raheem Sterling to fill their attacking void. The Chelsea loanee has battled for form and minutes so far this season.
"Well, he's been much more involved recently and his merit, he's earned the right to do so," said the manager. "All the players will have more exposure and he will have the right to do so."
Meanwhile, Arteta appeared to deny claims last night that Saka's hamstring injury would see him miss a further eight weeks.
Quizzed if Saka could return sooner to ease the burden, the manager continued: "It's too early, he's in early stage of rehab. When he's closer, doing more workload, we will see how he is."
Asked directly if there's been a setback in Saka's recovery, Arteta added: "No."
He also said, "Ben White is in training more regularly now. We have to manage his load, but he is available."
Arsenal will go to Leicester sitting in second-place, seven points behind leaders Liverpool. Leicester, meanwhile, sit 18th, two points from safety.
Arteta said of the Foxes: "Hopefully we will be better and better in coming weeks, but always we will adapt to the qualities of players we have available.
"They make life very difficult, I know Ruud (van Nistelrooy) well and the way he sets up his teams."