A male, 66, was quarantined at Majuro hospital on Thursday and is identified by health authorities as a "patient under investigation", said Health Secretary Jack Niedenthal in a statement.
Mr Niedenthal also called for donor assistance to provide laboratory-testing equipment so the islands have the ability to test for the coronavirus locally.
"This case is being treated and investigations are underway, including laboratory testing, to determine if this is a confirmed case of Covid-19."
He advised the public to remain calm and practice preventative measures.
He said a "person under investigation" designation only meant they had presented with some of the symptoms associated with Covid-19.
"It does not mean they have the disease," he added.
The individual, who is in quarantine at Majuro hospital, is a local resident who recently returned to Majuro from the US state of Washington, which is in the midst of a Covid-19 outbreak.
Authorities in Washington recently declared a state of health emergency. Covid-19 claimed 10 lives in Washington through Thursday this week.
Meanwhile, Palau announced its first suspected case Tuesday this week - a woman, 73, with an underlying health condition who travelled from the US state of Oregon with a medical mission.
She is currently isolated and under treatment at Belau National Hospital in Koror awaiting the results of testing from an off-island laboratory.
And both Fiji and Tonga have identified possible cases of Covid-19.
Most islands are stymied from a quick response to suspected cases by lack of laboratory equipment to test for the virus.
"We need lab testing capabilities and the expertise to set it up, like tomorrow, that should be priority number one," said Mr Niedenthal earlier this week.
He has been communicating this need for the US-affiliated islands including the Marshall Islands, Federated States of Micronesia and Palau to the US Centers for Disease Control, the Interior Department and the World Health Organization for the past several weeks.
Mr Niedenthal said those organisations were providing other assistance, but testing equipment was critical to fast diagnosis of possible coronavirus cases.
"If we know in a timely manner what we are dealing with here that would help us manage this situation much more effectively," he said.
The earliest the Marshall Islands will be able to confirm if the current patient under investigation has the coronavirus is expected to be Saturday or Sunday, depending on how quickly a Hawaii laboratory can complete the test result. Palau is similarly waiting for an off-island laboratory result to determine if the 73-year-old patient in Belau National Hospital has the virus.
Meanwhile, more than 1000 workers have been laid-off in the Northern Marianas due to the downturn in tourism caused by the coronavirus.
The Department of Labor said it had been notified that more than 1000 employees from various companies have lost their jobs.
Tourism has been decimated by plummeting visitor numbers from China, South Korea and Japan - three of the countries worst hit by the Covid-19 outbreak.
Peak season hotel occupancy rates on Saipan have plummeted from 95 to 23 percent.