Madueke opened the scoring in Wednesday's match with a thunderous strike in the 25th minute.
"Unbelievable goal. When you talk about individual quality and individual action and magic moments, that's it," Arteta told reporters. "A player that is able to pick the ball that far, dribble past people and finish with the quality and the power that he's done."
The 23-year-old then extended Arsenal's lead in the second half with a header from close range.
Madueke, who joined the club from Chelsea in July, has netted three times in two Champions League matches - the first in a 3-1 win over Bayern Munich last month following his return from a knee injury.
Madueke started on the right flank against Brugge, a position usually occupied by England international Bukayo Saka, and Arteta said some healthy competition between the two would help both players maintain a high level.
"They both have different qualities as well, and it's great because we're going to need them," the Spanish manager added.
"We are playing every three days, and players with that freshness and with that bite in the teeth as well. Understanding that they have to perform at their level, and this is the standard that we set. It's something really good...
"It's about consistency. It's not a game, it's two games, three games. It's when you do 10 games in a row every three days and that's the level that we have to hit."
Premier League leaders Arsenal next host Wolverhampton Wanderers on Saturday.
