Schaefer, 54, was found dead near a railway track on Saturday.
The Wiesbaden prosecution's office said they believe he died by suicide.
“We are in shock, we are in disbelief and above all we are immensely sad,” Bouffier said in a recorded statement.
Hesse is home to Germany's financial capital Frankfurt, where major lenders like Deutsche Bank and Commerzbank have their headquarters.
The European Central Bank is also located in Frankfurt.
A visibly shaken Bouffier recalled that Schaefer, who was Hesse's finance chief for 10 years, had been working “day and night” to help companies and workers deal with the economic impact of the pandemic.
“Today we have to assume that he was deeply worried,” said Bouffier, a close ally of Chancellor Angela Merkel.
“It's precisely during this difficult time that we would have needed someone like him,” he added.
Popular and well-respected, Schaefer had long been touted as a possible successor to Bouffier. Like Bouffier, Schaefer belonged to Merkel's centre-right CDU party. He leaves behind a wife and two children.
Editor's note: In this case we have decided to report on the subject of suicide. Telephone counselling services are available immediately in Germany for anyone who needs them. You can find help on free hotlines such as 0800-1110111 or 0800 3344533.