More than 47,000 people in the area were without power after the quake, reports said.
The moderate earthquake comes as Utah, along with every other state in the US, struggles to grapple with the impact of the novel coronavirus in the country.
The virus has now been detected in all 50 US states.
"I know the last thing we need right now is an earthquake, but here we are, and it sounds like aftershocks are likely," Salt Lake City Mayor Erin Mendenhall said on Twitter.
"The city is assessing the situation now and I'll circle back with an update when I have it. Be safe," Mr Mendenhall said.
The governor has urged people to stay away from the capital's downtown area.
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