Xhaka has skippered Emery's men in all six games he has played so far this season following the departure of Laurent Koscielny to Bordeaux.
However, Emery had held off on naming a permanent captain until he took a vote from his players, with Pierre-Emerick Aubameyang, Hector Bellerin, Alexandre Lacazette and Mesut Ozil making the rest of a five-man leadership group.
Xhaka, 27, has been fiercely criticised for his performances since joining the club in 2016 and was booed off by Arsenal fans when he was substituted during last weekend's clash with Aston Villa.
"First he's mature, he has experience," said Emery on Friday. "We are living under pressure, under criticism, as a coach, as a player, as a club. But really the most important thing is to stand up each moment, go ahead with his qualities, with his behaviour, with his commitment. In the dressing room the players voted him as the first (in the leadership group). I know, I spoke with him, we want to change that opinion outside. That respect he has inside is very, very important. Sometimes he makes mistakes. But the most important thing is to analyse, to learn and correct those mistakes."
Arsenal were trailing 2-1 to Villa when Xhaka was withdrawn before going on to win the game 3-2 despite being down to 10 men.
Many fans would like to see Xhaka dropped for a central midfield pairing of Matteo Guendouzi and Lucas Torreira and Emery said the captaincy will not influence his team selection.
"The performance is giving me the next first XI, the next players to play, not the captains," added Emery.
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