Robert Tesh, 32, is alleged to have made the threats against governor Gretchen Whitmer and Dana Nessel, the attorney general, to an acquaintance via social media on 14 April.
Mr Tesh, who was arrested later that day at his home, has now been charged with false report of threat of terrorism.
If convicted, he could face up to 20 years in prison.
Prosecutor Kym Worthy described the case as a “very disturbing scenario”, adding that threats against any public official carrying out their duties would not be tolerated.
Ms Worthy said: “You can disagree with their positions or their methodology, but you absolutely cannot act as this defendant allegedly acted or you will be charged criminally.”
Maria Miller, a spokeswoman for the Wayne County Prosecutor’s Office, said on Friday the threats were not specifically about the governor’s stay-at-home orders.
Prosecutors have not given specific details about the content of Mr Tesh’s messages or about which social media platforms he used to send them.
Ms Whitmer has received dozens of death threats posted on Facebook groups with thousands of members, some of whom appear to be linked to the armed protesters that have been demonstrating against lockdown outside the state Capitol in Lansing.
More protests are planned for this weekend.
Last week, the governor told ABC News that some lawmakers have decided to wear bulletproof vests as a precaution when they go to the state Capitol.
According to the Associated Press, the governor said on Friday: “It is never acceptable to make threats of violence to anyone, but our officeholders as well.”
She added that officials take threats “very seriously”.
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