Judge Jeffrey Sutton of the Sixth Circuit Court of Appeals wrote definitions of marriage should not be changed by the courts.
The 2-1 decision is the first at the appeals court level in favour of gay marriage opponents.
It affects Kentucky, Michigan, Ohio and Tennessee.
In recent months, four other appeals courts have struck down state bans on same-sex marriage, ruling they violated the US constitution's guarantee of equal protection under the law.
Last month, the US Supreme Court declined to hear challenges against those decisions, effectively ratifying them and leading to same-sex nuptials in several more states.
But the high court did not make its own ruling on the matter, in large part because at the time there was no dispute among the appeals courts.
Gay marriage is now legal in 32 states and in Washington DC.
On Tuesday, Judge Sutton and Judge Deborah Cook upheld the four state bans, arguing in their opinion that states had the right to set their own rules for marriage.
"Surely the people should receive some deference in deciding when the time is ripe to move from one picture of marriage to another," Judge Sutton wrote, adding the plaintiffs had not convinced the majority it should be the court's responsibility to intervene.
While the ruling said "gay couples, no less than straight couples, are capable of raising children and providing stable families for them" the judges argued marriages had been created an as "incentive for two people who procreate together to stay together for purposes of rearing offspring" and was "still relevant".
Judge Sutton also argued a constitutional right to same-sex marriage could be used in support of legalised polygamy.
"If it is constitutionally irrational to stand by the man-woman definition of marriage, it must be constitutionally irrational to stand by the monogamous definition of marriage," he wrote.
In a sharp dissent, Judge Martha Craig Daugherty wrote, "the author of the majority opinion has drafted what would make an engrossing TED Talk or, possibly, an introductory lecture in political philosophy.
"But as an appellate court decision, it wholly fails to grapple with the relevant constitutional question in this appeal."
Judge Daugherty suggested the majority had deliberately upheld the ban in order to force the Supreme Court to take up the matter.
"Because the correct result is so obvious, one is tempted to speculate that the majority has purposefully taken the contrary position to create the circuit split," she wrote, adding a Supreme Court ruling would put "an end to the uncertainty of status and the interstate chaos that the current discrepancy in state laws threaten".
In a statement, Evan Wolfson, president of pro-gay marriage group Freedom to Marry, said the decision was out of step with the majority of Americans.
"This anomalous ruling won't stand the test of time or appeal," Mr Wolfson said.
A lawyer for two of the couples represented in the case said he would appeal against the decision to the Supreme Court.
A US appeals court has upheld bans on gay marriage in four states, a ruling that increases the chances the Supreme Court will soon rule on the issue.