Benitez had made his debut for Qatar Stars League side El Jaish on Sunday before complaining of stomach pains and being rushed to hospital.
Valencia and Benitez were teammates at Ecuadorian club El Nacional from 2004 to 2005, with the pair clinching a Clausura title and making their Ecuadorean national team debuts in their second year together.
With tributes flowing in from around the world, Valencia posted several pictures of Benitez on social media accompanied by a series of emotional messages.
"Brother, God is with your family, we love you," Valencia tweeted from his official account.
"This strong pain you've caused me will stay forever my brother, but we love you.
"Please brother. Someone please say no."
Benitez, 27, spent the 2009/10 season on loan at then-English Premier League club Birmingham and several of his opponents at the time, including Lucas Leiva, Pablo Zabaleta and Craig Gardner, tweeted their condolences.
Birmingham paid tribute with an Instagram picture of the striker and posted that they will hold a tribute at their first Championship match on Saturday.
"RIP Christian 'Chucho' Benitez. Forever in our hearts," the club wrote.
"The thoughts of all at Birmingham City Football Club are with the friends and family of Chucho following this very sad news.
"The club will be looking to mark the passing of Chucho at St Andrew's ahead of this Saturday's fixture against Watford."
