Schumacher, a seven-time F1 champion who retired from the sport for a second time last year, is in an induced coma in intensive care at the University Hospital of Grenoble after hitting his head on a rock in a skiing accident in the resort of Meribel in the French Alps on Sunday.
Vettel has been dubbed 'Baby Schumi' by the German media after following the 44-year-old in becoming a multiple world champion.
"I am shocked and I hope that he gets better as quickly as possible," the four-time champion Vettel told www.bild.de.
"I wish his family much strength."
Vettel has credited Schumacher with being the inspiration behind his racing career.
Ferrari, with whom Schumacher won five world titles from 2000 to 2004, expressed their support in a statement on their official website.
It read: "Everyone at Ferrari has been in a state of anxiety since hearing about Michael Schumacher's accident.
"That includes the president, Luca Di Montezemolo, who through the Scuderia team principal Stefano Domenicali is in constant contact with the family and those close to the German champion.
"Montezemolo has offered his encouragement and support at this very difficult time, with the hope that better news will come soon."
The German raced for Mercedes for three seasons on his return to the sport following his first stint in retirement.
The German manufacturer said in a statement that their "thoughts and sympathies" were with him, his family and his friends.
It added: "We have been shocked to learn that he is in a critical condition and are closely monitoring the latest medical bulletins from Grenoble.
"We all know the depth of Michael's fighting spirit and send him all our strength and support in this latest battle.
"We sincerely hope that he will make a full recovery and will be with us again soon."
Angela Merkel, the German Chancellor, said she shared the shock of millions of Germans.
Her spokesman Steffen Seibert told the German media: "Like millions of Germans, the Chancellor and the members of the Federal Government were very shocked when they learned of Michael Schumacher's bad skiing accident.
"We hope, along with Michael Schumacher and his family, that his injuries will heal and he will recover. We wish his wife, his children and the rest of his family strength and mutual support."
The mayor of Schumacher's home town of Kerpen, near Cologne, also sent her support to the former racing driver.
Marlies Sieburg said in a statement: "My thoughts are with him and his family and I wish him together with the citizens of Kerpen all possible good wishes and a quick recovery."