The 20-year-old has struggled with an ankle injury suffered prior to last season but stepped up his comeback by playing 63 minutes of the Gunners' under-21 game at West Brom.
Wilshere came through the match unscathed and Burton was pleased with the midfielder's performance, and he told the club's official website: "It's like all players when they come back for their first game: they realise how difficult and tough it is. You always have to make that first step, and he has done that and that is fantastic."
Burton added: "He is a quality player, it is great for the club that he has taken that first step on the road towards getting back into the first team.
"I think he is delighted to have been back on the pitch, as we all are.
"It is a start, now he just needs to keep working hard to play the football we know he is capable of playing, which we know is very exciting.
"When he runs with the ball, it is very close to him and as he runs he always has his head up and is looking for opportunities to play people in.
"What you can't duplicate in training is that match sharpness and players coming in at you, so he will have benefited from that in this match."