"Ocean surface temperatures are already at record levels and our data indicate that the average temperature for all ice-free seas in May 2023 was higher than any other month of May," the service's deputy director said in a statement.
The findings are based on computer analysis of billions of data collected by satellites, ships, planes and weather stations around the world.
Some of the data used by Copernicus go back to 1950.
With regard to temperatures on the planet as a whole, the month of May was the second hottest ever recorded.
"May 2023 was the second warmest in the world, when we see signs of El Niño emerging in the equatorial Pacific", said Samantha Burgess, quoted by the agency France-Presse.
El Niño is a natural climatic phenomenon generally associated with an increase in temperatures, increased drought in certain parts of the world and heavy rainfall in others.
The phenomenon last occurred in 2018-2019 and gave rise to an episode of almost three years of La Niña, which causes opposite effects, namely a reduction in temperatures.
Despite this moderating effect, the last eight years have been the warmest on record.
In early May, the World Meteorological Organization (WMO), a specialized UN agency, warned of the likelihood of an El Niño occurring this year, raising temperatures to new records.