The Immigration Bill will make it a criminal offence to rent accommodation to illegal immigrants.
But shadow home secretary Andy Burnham told the Independent on Sunday it could cause problems for "anyone with a foreign-sounding name".
The Home Office said checks had to be made "on a non-discriminatory basis".
The bill, which returns to the House of Commons on Tuesday, includes the Right to Rent scheme.
This would see landlords required to carry out checks on prospective tenants, such as seeing their passport or visa, to ascertain their immigration status.
Failing to do so would be a criminal offence leading to a fine or a jail sentence.
Mr Burnham, describing the bill as "disproportionate, divisive, deceitful", said: "The aim of the Immigration Bill is to make Britain a 'hostile environment' for illegal migrants.
"In practice, it could end up making Britain a more hostile place for anyone with a foreign-sounding name."
Mr Burnham said society had advanced since landlords used to display discriminatory messages in their windows in the 1960s.
"But the new document checks could become the modern equivalent of the 'no dogs, no blacks, no Irish' signs and, by being more insidious, such casual discrimination will be far harder to challenge," he wrote.
He claimed the scheme was at odds with Prime Minister David Cameron's speech last week in which he raised the problem of young job-seekers with "white-sounding names" on their CVs getting a better response than others.
Mr Burnham asked: "If he truly believes what he was saying, why on earth is he about to legislate to make the same everyday racism far more likely to happen in the housing market?"
He said Labour would not "pander to prejudice" and called on Home Secretary Theresa May to rethink the plans.
A Home Office spokesman said: "The government has made clear that the Right to Rent scheme is about reducing illegal migrants' access to services - it has never been targeted at people with a lawful right to be in the UK.
"Right to Rent checks must be performed on a non-discriminatory basis - landlords are advised to check and record identity documents for all new tenants.
"Anyone who discriminates would be breaking the law."
Labour has accused the government of planning legislation that could cause "everyday racism" and "widespread discrimination" in the housing market.