The lawsuit, filed in US District Court, says the regulation is unconstitutional and violates religious freedom by targeting a Jewish ritual.
The rule, adopted unanimously by the New York City Board of Health last month, is aimed at reducing the risk that infants will contract herpes from the ancient ritual.
Using oral suction to take blood from the area of the circumcision wound is common in some of New York's ultra-Orthodox Jewish communities.
At least 11 boys caught herpes from the practice between 2004 and 2011, according to city health officials. Two of them died from the disease and two others suffered brain damage, they said.
Under the rule, parents must sign a consent form that says the health department advises that "direct oral suction should not be performed" because of the risk of contracting herpes.
The lawsuit says the city's conclusion that the ritual increases the risk of herpes is based on a flawed analysis and is not statistically sound.
"That opinion is based on limited study, inaccurate assumptions, and deficient data, all of which remain actively debated within medical and scientific communities," it says.
City Health Commissioner Thomas Farley defended the regulation.
"The city's highest obligation is to protect its children; therefore, it is important that parents know the risks associated with the practice," he said in a statement.
The plaintiffs include the Central Rabbinical Congress of the United States and Canada, the International Bris Association and several individual circumcisers, known as mohelim.
They want a judge to issue an injunction suspending the regulation.
The lawsuit says it violates the right to free speech because "the government cannot compel the transmission of messages that the speaker does not want to express."