Saka missed his side’s 1-0 Premier League win over champions Manchester City on Sunday with a hamstring injury.
England face Australia on October 13, before taking on Italy in a European Championship qualifier four days later.
“No, he will not make it,” said Arteta after Sunday’s game. “He has not trained for a single session.”
While he would not disclose the likely length of Saka’s spell on the sidelines, Arteta added: “He is not available to play football at the moment.”
Saka’s absence on Sunday ended a run of 87 consecutive Premier League games in which Arteta has played the 22-year-old winger.
He has been struggling with his hamstring in recent weeks, limping off during Arsenal’s 2-1 Champions League loss at Lens on Tuesday, and being withdrawn in last weekend’s victory at Bournemouth.
England manager Gareth Southgate said last Thursday he would take no risks with Saka, despite England being able to qualify for next summer’s European Championship during this international break.
“We’ve got that responsibility of qualifying for the country, but I’ve been a player. I’ve never ever taken a risk on a player’s physical wellbeing, and nor would I,” said Southgate.
“They [Premier League clubs] have trust in us that we make decisions that are right for the long term whenever we can.”
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