Blind said he needs a captain with more on-field presence as his team heads into two crucial European Championship qualifiers against Group A leader Iceland and Turkey.
"It's a great honor that the coach asked me to captain Oranje," Robben said in a written statement.
Robben was the undisputed star of the Dutch team that reached the semifinals of last year's World Cup in Brazil, but the Bayern Munich winger has struggled with injuries for much of the Euro 2016 qualifying campaign.
Van Persie, the Netherlands' all-time top scorer with 49 goals in 98 internationals, said he respected Blind's decision and accepted the role of vice-captain.
Blind, who replaced Hiddink last month after the veteran trainer's contract was terminated following a disappointing start to the Netherlands' qualification campaign, gave two teenage Ajax defenders, Jairo Riedewald and Kenny Tete, debuts in the national squad.
The youngsters have featured prominently in their club's strong start to the new season. Ajax has three wins from three matches in the Eredivisie and has yet to concede a league goal.
The Netherlands is third in qualifying Group A, five points adrift of Iceland and three points behind the Czech Republic.
The Dutch take on Iceland on Thursday at the Amsterdam Arena and travel to Turkey for Sunday's game in Konya.
Defenders: Jeffrey Bruma (PSV), Terence Kongolo (Feyenoord), Bruno Martins Indi (FC Porto), Jairo Riedewald (Ajax), Kenny Tete (Ajax), Stefan De Vrij (Lazio Roma), Gregory Van der Wiel (Paris Saint-Germain).
Forwards: Ibrahim Afellay (Stoke City), Memphis Depay (Manchester United), Klaas-Jan Huntelaar (Schalke 04), Luuk De Jong (PSV), Luciano Narsingh (PSV), Robin Van Persie (Fenerbahce), Quincy Promes (Spartak Moscow), Arjen Robben (Bayern Munich).