She made a statement to the House of Commons a day after a man drove a car into pedestrians on Westminster Bridge and then fatally stabbed a policeman.
PC Keith Palmer died trying to stop the attacker outside Parliament.
He was one of three people killed by the British-born man, who was then shot dead by police officers.
The other two victims were Aysha Frade, who worked at DLD College London, and a man in his mid-50s who has not yet been named by police.
Seven of the injured are still in hospital in a critical condition.
A further 29 had been treated in hospital, police said.
Addressing the House of Commons on Thursday, Mrs May said: "At approximately 2.40pm yesterday [14:40 GMT on Thursday] a single attacker drove his vehicle at speed into innocent pedestrians who were crossing Westminster Bridge, killing two people and injuring around 40 more.
"In addition to 12 Britons admitted to hospital, we know that the victims include three French children, two Romanians, four South Koreans, one German, one Pole, one Irish, one Chinese, one Italian, one American and two Greeks."
The Prime Minister said UK officials were in "close contact with the governments of the countries of all those affected".
The Irish Minister for Foreign Affairs, Charlie Flanagan, is aware that an Irish person was among the injured but did not provide any details about the casualty.
In a brief statement, Mr Flanagan said that his department has offered consular assistance through the Irish Embassy in London.
One Irish person is among about 40 people injured during the fatal attacks in Westminster, Prime Minister Theresa May has confirmed.