Sugarman also is the Vikings' infection control officer.
He said in a statement that he and his family immediately quarantined and "are all doing fine and experiencing only mild symptoms."
The Vikings said they are sanitizing their facility and contacted anyone who was in close contact with Sugarman. The team said those team personnel have been tested "and are returning under the established guidelines."
"Eric has not had recent contact with players, and no additional cases within the Vikings' front office have been identified at this time," the team said.
Minnesota did designate four members of its rookie class on the reserve/COVID-19 list Monday afternoon -- first-round wide receiver Justin Jefferson, sixth-round offensive tackle Blake Brandel, seventh-round safety Brian Cole II and undrafted free-agent offensive lineman Tyler Higby. None of the players, who reported to Eagan, Minnesota, for training camp last week, came into contact with Sugarman.
The reserve/COVID-19 list is for players who test positive for the coronavirus or were in close contact with an infected person or persons. The NFL has mandated that teams do not designate which category players fall into.
Sugarman will continue to serve as the Vikings' infection control officer virtually, the team said.
"I am humble to be serving in that capacity as it has been some of the most rewarding work of my career. But as I sit here in quarantine, it is clear this virus does not discriminate. It should continue to be taken seriously. I encourage people to take the necessary precautions and follow guidelines that have been established nationally and locally," he said in his statement.
The Vikings are moving forward with their mandatory reporting date for veterans on Tuesday in spite of Sugarman's positive test. All veterans are expected to show up on July 28 to receive their first of multiple COVID-19 tests before they will be allowed to enter TCO Performance Center for the first time for training camp.
ESPN's Courtney Cronin contributed to this report.