As of 12 June there had been 3,791 cases among more than 3.7m fully vaccinated people in the state, data from the Department of Public Health shows.
That means that around one in 1,000 fully vaccinated people in Massachusetts are still becoming infected despite getting their shots.
“We’re learning that many of the breakthrough infections are asymptomatic or they’re very mild and brief in duration,” Boston University infectious diseases specialist Davidson Hamer told The Boston Herald.
“The viral load is not very high. Breakthroughs are expected, and we need to better understand who’s at risk and whether people who have a breakthrough can transmit the virus to others,” he continued.
“In some cases, they’ll be shedding such low levels of the virus and won’t be transmitting to others.”
The Centers for Disease Control has stated that the three vaccines available in the US prevent most people from getting the virus.
But the CDC has also recognised that there will be “a small percentage of fully vaccinated people who still get sick, are hospitalised, or die from Covid-19”.
Data shows that Moderna and Pfizer’s vaccines are around 90 per cent effective against infection, two weeks after the final dose.
And the one-shot Johnson & Johnson shot is 72 per cent effective in preventing moderate to severe cases of Covid-19.
All three vaccines completely prevent hospitalisations and deaths, according to their trial results.
The CDC says that more than 150m Americans are now fully vaccinated, and more than 65 per cent of adults in the country have had at least one dose.
More than 33.5m Americans have tested positive for Covid-19, and 602,000 people have died during the pandemic.