The daily average for hospital admissions has risen past 100,000 for the first time since last winter.
The recent wave, driven by the Delta variant, is most severe in the US South but cases are rising nationwide.
Monday's guidance from the 27-nation bloc reverses advice from June that lifted restrictions on American travellers ahead of tourism season.
The recommendation is nonbinding, meaning individual countries will be allowed to decide if they still wish to allow US visitors with proof of vaccination, negative tests, or quarantine.
Though the EU first lifted travel restrictions on Americans in June, the US has kept their ban on European non-essential travel in place since March 2020.
Earlier this month, European Commission President Ursula von der Leyen said the lack of reciprocity would not be allowed to "drag on for weeks".
Israel, Kosovo, Lebanon, Montenegro, and North Macedonia have also been removed from the EU's safe travel list.
Hospital admissions in the US for Covid-19 patients have reached levels not seen since January, when the country reached its all-time high with more than 142,000 coronavirus patients in hospital beds.
Florida has more than 16,000 Covid-19 patients in hospital - the most of any state - followed by Texas and California, according to data from the US Department of Health and Human Services.
The latest surge is straining hospitals and health care workers. Roughly one in five intensive care units have reached at least 95% capacity.
Death rates have risen too - reaching an average of more than 1,000 per day. Just over half of all Americans are fully vaccinated against Covid-19.
With the full approval of the Pfizer vaccine by the US Food and Drug Administration last week, the Biden administration has doubled down on its efforts to increase vaccination rates.
Unvaccinated people are about 29 times more likely to be admitted to hospital with Covid-19 than those who are fully vaccinated, according to a study released by the US Centres of Disease Control and Prevention (CDC) last week.