Odegaard was confirmed as the club's skipper before the start of the new season, having worn the armband during the closing stages of the previous campaign.
The 23-year-old appears to be revelling in the role, scoring three goals in the last two games and leading the Gunners to four wins from four in the Premier League so far this season.
"He's more humble I would say - even more," Arteta replied when asked if he had seen a change in the Norway captain since giving him the armband.
"That's the way he is. More humble and more hungry, a good combination. At 23 he has already had a lot of experience and a lot of pressure, especially individually.
"He's played for Madrid and knows what it's about. He does it all natural, nothing worries him, and he's developing that even more."
Aston Villa are the visitors to the Emirates Stadium on Wednesday night as they look to get their season on track while derailing Arsenal's perfect start.
Arteta will be without midfield duo Thomas Partey and Mohamed Elneny for the game, the latter suffering a hamstring injury against Fulham having been drafted with Partey sidelined due to a thigh issue.
Eddie Nketiah made a difference after coming off the bench in the 2-1 win over the Cottagers, Arsenal coming from a goal behind to maintain their run.
The record goalscorer for England Under-21s has yet to start a game this season after agreeing a new deal in the summer.
But Arteta insists he would have no qualms bringing Nketiah into his side to face struggling Villa.
"He is a threat, every single day in training," added the Arsenal boss.
"You ask him to play and immediately the boy is ready. He has no fear. He's confident, he has power and the boys really believe in him.
"We changed the formation and got in better connection and spaces.
"They are a really physical team, a lot of presence and very good and dangerous in the box. It will be tough."