The 28 year old played the full duration of the 3-2 defeat against world champions Spain before missing both clashes against Czechia and Croatia.
England will face Czechia once more on Tuesday night and once again without Konsa who has now departed the camp as he made his way back to North London this week.
Reports state that Konsa could be okay to face Leeds United this weekend as club football returns but England boss Thomas Tuchel revealed that it may not be that simple as the defender has suffered trauma.
"Ezri felt discomfort when he came into camp," Tuchel told reporters. "He played with discomfort against Spain and it got a bit worse so he stayed in camp and tried everything for the match in Czechia which came too soon.
"He tried everything for the match in Croatia and gave the green light, finished all the training sessions, unfortunately he got another hit on the quad that caused a light trauma.
"We decided to not let him play through the pain and discomfort again, so he left camp to get treatment for both of his issues.
"I think nothing major but not worth the risk taking. We were happy with attitude that he showed to stay in camp. It's a knock not a muscle injury."
Konsa has started three of the Gunners' opening five Premier League games since his £50M summer move from Aston Villa. The Gunners next face Leeds, Lille, Nottingham Forest and Bayern Munich over the next two weeks in what is a tough schedule.
The good news for the Premier League champions is that Ben White and Cristhian Mosquera are now back in contention, whilst Jurrien Timber is very close to being back for manager Mikel Arteta.