The statement was released by Downing Street yesterday evening, stating Mrs May does 'not agree' with Donald Trump's travel ban on refugees and citizens of seven mainly-Muslim countries and she will make representations if it hits Britons.
But the Doncaster North MP has criticised the Prime Minster for only deciding to speak out now.
Commenting on Twitter, ex-Labour leader Mr Miliband called the statement 'far too late and far too weak'.
Prior to the statement being released, Mr Miliband said: "It is beyond appalling and shameful that the Prime Minister of his party believes even for a moment that she can stay silent."
The Prime Minister arrived back in Britain to a storm of fury after she refused to condemn the US president's controversial ban, which could affect UK citizens born abroad.
Conservative MPs were among the critics and one claimed he would be affected by the border clampdown, which targets those from Iraq, Iran, Libya, Somalia, Sudan, Syria and Yemen.
Hours after Mrs May arrived back from a visit to Turkey, No 10 moved to stem the growing anger.
A spokesman said: "Immigration policy in the United States is a matter for the government of the United States, just the same as immigration policy for this country should be set by our government.
"But we do not agree with this kind of approach and it is not one we will be taking.
"We are studying this new executive order to see what it means and what the legal effects are, and in particular what the consequences are for UK nationals.
"If there is any impact on UK nationals then clearly we will make representations to the US government about that."
Mrs May was pressed repeatedly about her views on the refugee ban during a press conference in Ankara where she had been holding talks with Turkish leaders.
After initially dodging questions, the Prime Minister then insisted it was up to America to devise its own policy.
She told reporters: "The United States is responsible for the United States' policy on refugees.
"The United Kingdom is responsible for the United Kingdom's policy on refugees and our policy on refugees is to have a number of voluntary schemes to bring Syrian refugees into the country, particularly those who are most vulnerable, but also to provide significant financial contributions to support refugees in countries surrounding Syria."
But her decision to keep quiet about the actions of President Trump, who she met for talks in Washington on Friday, was roundly criticised.
Conservative MP Nadhim Zahawi, who is of Iraqi origin but a British citizen, said a US immigration lawyer had confirmed that he would be affected by the ban.
"A sad sad day to feel like a second-class citizen," he said. "Sad day for the USA.
"Had confirmation that the order does apply to myself and my wife as we were both born in Iraq. Even if we are not dual Nat.
"I'm a British citizen and so proud to have been welcomed to this country. Sad to hear ill be banned from the USA based on my country of birth."
There are fears that British athletes including Sir Mo Farah, who trains in the US and was born in Somalia, and former Team GB basketball player Luol Deng could be affected by the ban.
Olympic champion Sir Mo, 33, lives with his wife and children in Portland, Oregon, but is believed to be currently training in Ethiopia.
The NBA has asked the US government to clarify whether Sudan-born Deng, 31, who plays with the Los Angeles Lakers, will be affected.
Tory MP Heidi Allen rounded on Mrs May for the way she had handled the situation.
She said on Twitter: "Strong leadership means not being afraid to tell someone powerful when they're wrong. It's an ethos this country is proud of @theresa_may.
"I don't care how special the relationship is, some lines just shouldn't be crossed."
Labour leader Jeremy Corbyn said the refusal to speak out should "sadden" the country and the Lib Dems said it was "shocking".
Scottish Tory leader Ruth Davidson said the ban was "both wrong in itself and very worrying for the future".
The US president has barred all refugees from entering the US for four months but blocked those from war-ravaged Syria indefinitely as part of a plan to stop "radical Islamic terrorists".
A 90-day ban on entry to the US from the seven Muslim-majority nations has been imposed.
Speaking in the White House, Mr Trump said the ban was "working out very nicely".
He said: "It's not a Muslim ban but we were totally prepared. It's working out very nicely.
"You see it at the airports, you see it all over, it's working out very nicely, and we are going to have a very, very strict ban and we are going to have extreme vetting, which we should have had in this country for many years."
Canada's prime minister Justin Trudeau said his country welcomed "those fleeing persecution, terror and war", regardless of their faith.
Tory MP Sarah Wollaston said Mr Trump must not be invited to address both houses of Parliament from Westminster Hall on his state visit later this, pointedly insisting "those who wish to fawn over him" should do so elsewhere.