The Labour leader said Theresa May should not be endorsing Mr Trump until it was clear his Government was "actually going to protect fundamental rights and freedoms and laws".
Ms May invited Mr Trump to Britain on behalf of the Queen when she visited him
in Washington DC earlier this week. He accepted her invitation.
The Prime Minister refused to condemn the ban on Saturday when questioned by journalists. The policy affects British citizens who were born in Iraq, including Conservative MP Nadhim Zahawi, who says it will prevent him visiting his children in America.
After sustained criticism, in the early hours of Sunday morning Downing Street issued a statement saying Ms May was in fact opposed to the ban, though she has yet to personally comment on the matter.
Mr Corbyn told ITV1's Peston on Sunday programme: "It’s slightly odd he should be invited so quickly and particularly in view of the statements that he’s made. I suspect this visit is something that might find its way into the long grass.
"I think we need to find out exactly what his intentions are and how much the US parliamentary system is actually going to protect fundamental rights and freedoms and laws.
Theresa May repeatedly refuses to condemn Donald Trump immigration ban
"Is it really right to endorse somebody who has used this awful misogynist language throughout the election campaign, awful attacks on Muslims and then this absurd idea of building a wall with their nearest neighbour?"
Sources close to Mr Corbyn say the Labour leader also believes a visit would be inappropriate while Mr Trump’s separate order banning Syrian refugees remains in place.
Speaking after the progamme Mr Corbyn added: "Donald Trump should not be welcomed to Britain while he abuses our shared values with his shameful Muslim ban and attacks on refugees' and women's rights.
"Theresa May would be failing the British people if she does not postpone the state visit and condemn Trump's actions in the clearest terms. That's what Britain expects and deserves."
MPs previously debated banning Mr Trump from the UK at the start of last year after a petition on the matter garnered around half a million signatures, triggering a discussion in Parliament. No action was taken after the debate, however.
Protesters are set to assemble outside Downing Street at 6pm on Monday to criticise Ms May's response to the attacks on British citizens.
That gathering will come after protests at New York's JFK airport, as well as a strike by some NYC taxi drivers covering journeys to the airport.