Same-sex marriage sets a "dangerous precedent" which could lead to sibling marriage or polygamy, says Lord Carey.
Ahead of the Lords debate on the bill next week, the former archbishop of Canterbury argued there could be "unintended consequences".
He has previously courted controversy by likening critics of gay marriage to persecuted Jews in Nazi Germany.
Gay rights group Stonewall said the comments were "regrettable" and accused the peer of "hyperbolic shroud waving".
Lord Carey has been a vocal opponent of the government's Marriage (Same Sex Couples) Bill for England and Wales, which will be debated by peers on Monday.
It is expected to face a tough passage through the Lords - crossbench peer and former West Midlands chief constable Lord Dear has tabled an amendment to refuse it a second reading - which if passed would effectively kill the bill.
The government has confirmed that if the Lords debate over-runs, the vote will be carried over until the next day, amid warnings that - with 86 peers asking to speak - it could be otherwise be lost in the early hours of Tuesday morning.
In an article for the think tank Civitas, Lord Carey, who is a member of the House of Lords, argues that the government is effectively seeking to change the definition of marriage to "a long-term commitment between two people of any sex, in which gender and procreation are irrelevant".
He says he does not want to be "alarmist", but that could logically be extended to "say, two sisters bringing up children together" or "multiple relationships, such as two women and one man".
"Ultimately, the proposed legalisation of same-sex marriage represents a paradigm shift in our understanding of marriage," he argues.
It is not the first time the former Archbishop of Canterbury has suggested that legalising same-sex marriage could pave the way for polygamy - suggesting at the Conservative Party conference last year that there was a "slippery slope" to allowing a "Mormon-style relationship".
The Department for Culture, Media and Sport said it did not want to respond directly to Lord Carey's comments.
But Stonewall chief executive Ben Summerskill said: "This is regrettably hyperbolic shroud waving.
"We pray other peers will be a little more attuned to the 21st Century during next week's debate."
On Thursday the Bishop of Salisbury, the Rt Rev Nicholas Holtham suggested in a letter to the Telegraph that it was time to "rethink" attitudes about same-sex marriage, as Christians had done with slavery and apartheid.
"No one now supports either slavery or apartheid. The Biblical texts have not changed; our interpretation has."
He argued that same sex marriage did not "detract from heterosexual marriage" and that the "development of marriage for same sex couples is a very strong endorsement of the institution of marriage".
The bill would allow same-sex couples, who can currently hold civil ceremonies, to marry.
Religious organisations would have to "opt in" to offering weddings, with the Church of England and Church in Wales being banned in law from doing so.
It is backed by Prime Minister David Cameron, his Lib Dem deputy Nick Clegg and Labour leader Ed Miliband and 366 MPs, but it was opposed by 161 MPs in a free vote in the Commons, 133 of them Conservative.
Mr Cameron hopes it will become law soon, with the first ceremonies taking place by next summer.
The Scottish government has confirmed it will introduce a bill shortly to allow same-sex marriage.