Thomas Schaefer, a member of Chancellor Angela Merkel’s Christian Democratic Union, was found on railway tracks at Hochheim, near Frankfurt, on Saturday.
Police and prosecutors said that the evidence, including witness statements and examination of the scene, led them to conclude the 54-year-old killed himself.
State governor Volker Bouffier said Schaefer had worked “literally day and night” to deal with the Covid-19 crisis.
“We have to assume that he was very worried,” said Mr Bouffier. “Above all, there are great concerns about whether it will be possible to meet the huge expectations of the population – especially financial aid.
“I have to assume that these concerns overwhelmed him. He obviously couldn’t find a way out. He was desperate and left us. His death is also a great loss for this country.”
Schaefer had been Hesse’s state finance minister for a decade and was seen as a potential candidate for the region’s next governor.
The Hesse CDU party said in a statement that it was in mourning, adding: “We heard with dismay the news of his sudden and unexpected death. Our thoughts are with his family and relatives.”
Germany has reported 455 deaths and more than 58,000 confirmed cases of Covid-19 since the start of the outbreak.