After 10 years with Sevilla, the right winger moved to Manchester City earlier this month for a fee of around £15million.
The 27-year-old could win his 28th cap for Spain in Sunday night's Confederations Cup final against Brazil at the Maracana in Rio de Janeiro.
His international team-mate Iniesta believes new City boss Manuel Pellegrini has picked up "a very special player" who can be likened only to Tottenham star Bale, the winner of the PFA Player and Young Player of the Year and FWA Footballer of the Year awards last season.
"He's going to cause the defences in the Premier League a real problem when he plays for City," Iniesta told the Sunday Mirror.
"Jesus has so much speed, and his feet are so quick, that it becomes nearly impossible to stop him without fouling him.
"The only player that I can compare him with that is already playing in England is Gareth Bale."
Navas created 76 chances for his Sevilla team-mates over the course of last season in La Liga, the fifth highest total in the Spanish top-flight.