Iniesta ended a career-long association with Barca at the end of last season to join Vissel Kobe in the J-League.
Brazil midfielder Arthur, newly arrived from Gremio, took the Spain great's number eight shirt and has stepped up impressively to lend an air of continuity in Barca's engine room.
"I think that just watching him play everybody realises that he is a player who has a strong personality, who always knows what to do with the ball," Iniesta told DAZN.
"He is young, he also needs a process of adaptation to the team and, nevertheless, it is already seen that he is very attuned with that type of game.
"Surely he is growing with the passage of time, surrounded by people who have a lot [of capacity] to grow."
Arthur's absence due to a hamstring injury has been felt by a Barca side who have turned in some below-par performances of late.
But the 22-year-old is back in Ernesto Valverde's squad for Wednesday's Copa del Rey semi-final against Real Madrid, with the tie locked at 1-1 after the first leg at Camp Nou.
In a tight, high-stakes contest, Iniesta believes Dembele – another Barcelona player to have become influential despite injury setbacks – has the qualities to come to the fore.
"Ousmane is a different player, a player who can decide any game at any time," he added.
"He is a very fast player, very skilled, very direct and at Barca that type of player is great.
"This year he is scoring goals regularly. It's a pity about some injuries that he's has had, but surely he will be an important player in the next years."
A second Madrid-based Clasico in the space of four days arrives on Saturday, with Barcelona nine points better off than their bitter rivals in LaLiga.
Victory would be seen by many as decisive in the destination on the title but Iniesta maintains Atletico Madrid – second and seven points back – should not be ruled out of contention.
"Undoubtedly, Barca has a certain advantage, but in February it is difficult to decide a league," he said.
"There are many matches left, then comes the Champions League, which is also an added strain. It is always a very competitive league until the end, we will see in the last section how it ends."
On whether this weekend's Clasico will be decisive, Iniesta added: "There's also Atletico Madrid out there and, if I'm not mistaken, the closest one now is Atletico."