On Wednesday, the comedian shared a photograph on her Twitter and Instagram accounts of herself lying in a hospital bed wearing a face mask.
In the caption, the 59-year-old said she had been sent to an isolation ward after visiting an urgent care facility.
Despite experiencing symptoms consistent with the coronavirus, Griffin said her attempts to get tested had proved unsuccessful.
The star blamed Mr Trump and Vice President Mike Pence saying they had not made enough tests available in the USA, and shared a tweet from President Trump saying the country had more testing than any other nation.
“I was sent to the #COVID19 isolation ward room in a major hospital ER from a separate urgent care facility after showing UNBEARABLY PAINFUL symptoms.
“The hospital couldn’t test me for #coronavirus because of CDC (Pence task force) restrictions. #TESTTESTTEST.”
In the initial tweet posted by Mr Trump, the president boasted about the large number of Americans currently being tested for coronavirus, writing: “Just reported that the United States has done far more 'testing' than any other nation, by far.
”In fact, over an eight day span, the United States now does more testing than what South Korea (which has been a very successful tester) does over an eight week span. Great job!"
Just reported that the United States has done far more “testing” than any other nation, by far! In fact, over an eight day span, the United States now does more testing than what South Korea (which has been a very successful tester) does over an eight week span. Great job!— Donald J. Trump (@realDonaldTrump)March 25, 2020
According to the BBC, the latest data shows that 359,161 people have been tested in the US.
While this is marginally more than the amount of people tested in South Korea, it is important to note that the US has a population of 328 million, compared to around 51 million in East Asian nation.
The number of confirmed cases of Covid-19 continues to grow in the US, with 69,117 so far. However, the true number of cases is likely to be significantly higher.
In January, Mr Trump told CNBC he was “not at all” concerned about the virus, saying: “It’s going to be just fine … we have it totally under control.”
However, the president later wrote in a tweet that he had “always” taken Covid-19 seriously, referring to it as the “Chinese virus” and adding: “The Fake News new narrative is disgraceful [and] false!”