The Labour leader hit out as a leaked EU document suggested that other countries could adopt a tough approach on the issue because of the difficulties their citizens may face acquiring permanent rights in the UK.
Theresa May will face a challenge to her approach on the issue in the House of Lords over the coming weeks as Labour and Liberal Democrat peers attempt to rewrite the Bill giving her permission to trigger Article 50 and start the Brexit process.
She has repeatedly said she wants to guarantee the rights of EU citizens in the UK - but only if reciprocal arrangements apply to Britons living in other member states.
A leaked document drawn up by the European Parliament's legal affairs committee, obtained by the Guardian, said it will be down to each member state to decide whether British citizens are allowed to carry on living within their borders after 2019.
It notes: "The fact that it appears to be particularly difficult for foreign nationals, even if married to UK nationals or born in the UK, to acquire permanent residence status or British nationality may colour member states' approach to this matter."
Mr Corbyn told the Guardian the document showed "the human cost of a Tory-style Brexit".
"Families, jobs and homes are all in the balance," he said.
"There must be an end to this Hunger Games approach to Brexit negotiations, which gives no consideration to EU nationals in our country or British nationals living abroad."
Lib Dem leader Tim Farron said: "This issue could have been settled from the start if the Government had done the right thing and made clear EU citizens who have made the UK their home can remain indefinitely.
"Instead, millions of people on both sides of the channel are being left in limbo and faced with agonising uncertainty over their futures.
"Antagonising our European partners is no way to get a good deal for Britain and for the many UK citizens living in EU countries."
Dutch MEP Sophie in 't Veld said the situation was "unacceptable" and the 4.5 million citizens affected - more than three million EU nationals in the UK and over a million Britons on the continent - were not "bargaining chips".
The document was drawn up by the European Parliament's committee on legal affairs this month, the newspaper said.
In a foreword to the report, Pavel Svoboda, the Czech chairman of the committee, writes: "One important preliminary question affecting all policy areas is the extent to which transitional arrangements could be envisaged legally.
"It would seem to us that such arrangements could only be adopted by international agreement or a protocol to the treaties, which would require the unanimous agreement of the member states and ratification in accordance with their national constitutional tradition.
"It would seem difficult, if not impossible, to reach such an agreement before the end of the period provided for in Article 50."
A Home Office spokesman said: "This Government has been clear, that we want to protect the status of EU nationals already living here and the only circumstances in which that wouldn't be possible is if British citizens' rights in European member states were not protected in return.
"The Prime Minister has reiterated the need for an agreement as soon as possible as part of the negotiations to leave the EU."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies