The 20-year-old impressed in Friday's 4-0 victory against Lithuania, netting his first senior goal for the Three Lions in a one-sided Euro 2016 qualifier.
Sterling will not, though, be travelling with Roy Hodgson's side to Turin as an ongoing toe issue has ruled him out of Tuesday's friendly against Italy.
The winger – like James Milner, Leighton Baines and Danny Welbeck – has returned to his club, who next Saturday face a crucial match in the fight for the top-four.
"It had been pre-agreed with the FA and obviously my club to get an injection after the game," he said. "I will receive some treatment back at the club and go from there."
Asked if he would be okay for the trip to Arsenal, Sterling said: "Hopefully, yeah.
"I will get this injection now and see how it goes in the next few days. Hopefully I will be okay for the Arsenal game."
It is a match Sterling will approach buoyed by a memorable night in front of a sell-out Wembley crowd.
Lost amidst the excitement of Harry Kane's goalscoring debut was the fact that the Liverpool attacker's close-range effort was his first for England, coming on his 14th appearance.
"Yeah, definitely (it has preyed on my mind) but obviously that's part of the game," Sterling said.
"You've got to keep on and when a chance comes along, you've got to take it. Hopefully now I can continue to progress with England.
"Obviously it is good to get a win for England and good to get my first goal. It is a massive win for the team."
The goal was all the more special for Sterling given he grew up in the shadows of Wembley Stadium.
"It's been a long time coming to get my first goal, but I'm really happy and hopefully I can continue this with England," he said.
"I watched this stadium get built, so it was obviously pleasing to score at Wembley. It will live with me for a long time."