It means he will be unable to meet US President Joe Biden later on Thursday as part of the traditional shamrock ceremony.
Mr Martin had been due to speak at the 30th anniversary of the Ireland Funds Gala dinner on Wednesday evening.
He has now left that gathering.
Mr Martin’s speech was instead given by Irish Ambassador to the US, Daniel Mulhall.
“I know you will all join with me in wishing the Taoiseach a speedy recovery,” he told the audience in Washington.
It remains unclear how the White House St Patrick’s Day celebrations will now be handled – if someone will take Mr Martin’s place or if the meeting will be carried out virtually instead.
It also casts doubt on whether the Taoiseach can return to Ireland for a national day of remembrance on Sunday to commemorate those who died during the Covid-19 pandemic.