The Ecuador international, 27, was taken to hospital on Monday complaining of stomach pains and suffered a fatal heart attack.
Benitez had made his debut for Qatar Stars League side El Jaish Qatari El Jaish on Sunday in their 2-0 win over Qatar SC in the Sheikh Jassem Cup.
"Saddened by the death of Chucho Benitez. My thoughts are with his family and Ecuadorian Football," posted Blatter on Twitter.
English Championship club Birmingham City also honoured the striker.
Benitez enjoyed a year-long spell at Birmingham during the 2009-10 season, scoring four goals in 36 appearances for the club.
A statement of the club's official website read: "Birmingham City Football Club is saddened to learn of the passing of former striker Christian 'Chucho' Benitez.
"The thoughts of all associated with the football club are with Chucho's family and friends at this very sad time.
"The Ecuador international was an immensely popular character during his time at the football club."
Former Birmingham team-mates Liam Ridgewell and Craig Gardner, who now play for West Brom and Sunderland respectively, took to Twitter to offer their condolences.
"Can't believe the news about Chucho. Such a sad thing. Had a great yr (year) with him at blues. Sad time, my thoughts go out to his family RIP," wrote Ridgewell.
Gardner added: "Can't believe Christian Benitez aka chucho has died had the pleasure to play with him he was a top bloke. My thoughts go out to his family."
A host of Premier League stars also voiced their shock at the news on the social networking site.
"Extremely sad and shocked by the death of Chucho Benitez, my thoughts and prayers go out to his family and friends #animoEcuador," tweeted Manchester United striker Javier Hernandez.
Hernandez's Old Trafford team-mate Rio Ferdinand wrote: "RIP Christian Benitez, sad to hear the terrible news."
Manchester City defender Pablo Zabaleta added: "Very sad to hear that Ecuadorian player Christian Benitez was killed. My deepest condolences to his family."
"What horrible news!! RIP Christian Benitez," commented Liverpool midfielder Lucas Leiva.
Sunderland defender Carlos Cuellar tweeted: "Sad news of the death of player Chucho Benitez my deepest condolences to his family and the people of Ecuador."
