The state minister for foreign affairs Olivier Nduhungirehe confirmed the border closure to The Associated Press on Thursday.
There appeared to be no link between the man's case and the previous one in Goma, Jean-Jacques Muyembe, a local Ebola response co-ordinator, told reporters.
The WHO, which declared this year-long Ebola outbreak a global health emergency last month, has recommended against travel restrictions.
World Health Organization has recommended against travel restrictions amid the outbreak but says the risk of regional spread is "very high".
Earlier on Thursday, a DRC official said the one-year-old daughter of the man who died on Wednesday was at a treatment centre after showing signs of the disease.
The emergence of the disease in Goma is a particular concern because experts fear the disease could spread out of control in this sprawling, densely-packed city.
To mark Thursday's first anniversary of the current outbreak being declared, United Nations agencies issued a joint statement on Wednesday, saying there have been more than 2,600 confirmed cases, including more than 1,800 deaths, in parts of DRC's Ituri and North Kivu provinces. "Most of the women here cross into Rwanda to find food for us in Goma", he said.
The man arrived in Goma on July 13 and started showing symptoms on July 22. He had spent five days being treated at home and then went to a health facility, where Ebola was suspected. That patient was a pastor who had left South Kivu to evangelize in Butembo, a center of the current Ebola outbreak.
Rwanda has reopened its border with the Democratic Republic of Congo after closing it for several hours, a reaction to three Ebola cases, two of them fatal, in a border city in the past month.
June 4: The outbreak surpasses 2,000 confirmed Ebola cases.
Over 5000 health workers have been vaccinated against Ebola in Goma, DRC. The World Health Organization has declared the Ebola outbreak an worldwide emergency. Containing the outbreak faces unprecedented challenges amid attacks by rebel groups and resistance by wary community residents in a region of Congo that had never experienced an Ebola outbreak before.
The designation has only been used four times previously, including during the Ebola epidemic that killed more than 11,000 people in West Africa between 2014 and 2016.