He said “stronger protections” were needed to end “the merry-go-round of legal challenges which risk paralysing the scheme”.
The government said the bill, unveiled earlier, made clear in UK law Rwanda was a safe country for asylum seekers.
But it stops short of what some on the Tory right were demanding.
In his resignation letter to Rishi Sunak, Mr Jenrick said the prime minister had “moved towards my position” on the emergency legislation.
“Nevertheless, I am unable to take the currently proposed legislation through the Commons as I do not believe it provides us with the best possible chance of success.”
Mr Jenrick added that the bill was “a triumph of hope over experience”.
In response, the prime minister described Mr Jenrick’s resignation as “disappointing” and “based on a fundamental misunderstanding of the situation”.
“If we were to oust the courts entirely, we would collapse the entire scheme,” Mr Sunak said.
“The Rwandan government have been clear that they would not accept the UK basing this scheme on legislation that could be considered in breach of our international law obligations.”
The plans to send some asylum seekers to Rwanda aim to deter people from crossing the English Channel in small boats.
But the scheme has been repeatedly delayed by legal challenges and no asylum seekers have been sent to the east African country from the UK so far.
Mr Jenrick, who had supported Mr Sunak’s leadership campaign, said the emergency legislation was the “last opportunity” to prove the government would do “whatever it takes” to stop small boat crossings.
Losing a minister who was once a key ally is a blow for Mr Sunak, in a week when the government had been trying to get on the front foot on migration.
Labour’s shadow home secretary Yvette Cooper said: “It is a sign of the total chaos in the Tory party and the complete collapse of Rishi Sunak’s leadership that even while he is sitting in the Commons for the announcement of his new Rwanda plan, his own immigration minister is resigning because he doesn’t think it will work.”
Senior figures are musing privately that they would not be surprised if Mr Sunak ended up facing a confidence vote from his own MPs.
Although it may not come to that, it is a measure of the bleak mood among many Conservatives.
Reports of Mr Jenrick’s resignation first started swirling after the government published the draft bill.
The legislation aims to address the concerns of the UK’s Supreme Court, which last month ruled plans to send some asylum seekers to Rwanda were unlawful.
The bill – which must be approved by Parliament – orders the courts to ignore key sections of the Human Rights Act in an attempt to sidestep the Supreme Court’s existing judgement.
It also orders the courts to ignore other British laws or international rules – such as the international Refugee Convention – that stand in the way of deportations to Rwanda.
However, it does not go as far as some Tory MPs wanted.
Former Home Secretary Suella Braverman and her supporters had called for it to override the entire Human Rights Act, the European Convention on Human Rights (ECHR), the Refugee Convention, and all other international law.
The bill allows ministers to ignore any emergency order from the European Court of Human Rights in Strasbourg to temporarily halt a flight to Rwanda while an individual case is still being considered.
But it stops short of providing powers to dismiss the whole of the ECHR.
It also allows migrants to legally challenge their removal to Rwanda on specific individual grounds, if they can prove that being put on a plane would leave them at real risk of serious harm.
A source close to Mrs Braverman said the bill was “fatally flawed” and would be “bogged down in the courts for months and months”.
However, if the government had agreed to her demands this would have provoked a backlash from centrist Tories.
The One Nation group, which is made up of more than 100 Tory MPs, had warned that overriding the ECHR was a “red line” for a number of Conservatives.
The group cautiously welcomed “the government’s decision to continue to meet the UK’s international commitments which uphold the rule of law” but added that it would seek legal advice “about concerns and the practicalities of the bill”.
The draft legislation concedes that it may not be compatible with the ECHR.
This means government lawyers have told ministers the measures could still be legally challenged.