While both players travelled to the US as part of the club’s preseason tour, neither were involved during the games against Everton, Orlando City and Chelsea.
Arsenal play only one more friendly before their Premier League season opener against Crystal Palace, although there is a hope both players will soon return to full training.
Tomiyasu impressed during his first season at the club but struggled with injuries at times, while summer signing Vieira is yet to make his debut following a £34m move from Porto.
Arteta confirmed Tomiyasu is close to a return to training, although Vieira – who was spotted wearing a protective boot not long after signing – is slightly further behind in his recovery from injury.
Speaking after Arsenal’s 4-0 win over Chelsea in Orlando, Arteta said: “Tomi is really close to start doing some training sessions.
“Hopefully next week and Fabio probably a little bit longer.
“I think he needs another week or so before he starts with the team but he’s been working hard and he’s been really unlucky to start his Arsenal career in this way but again he’s fitting in well.”