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6 year oldTheodore McCarrick, 88, a former Archbishop of Washington, must also carry out "penance and prayer" pending a canonical trial, the Vatican said.
Last month US Church officials said the allegations were credible.
Mr McCarrick has said he has "no recollection" of the alleged abuse. Further allegations have since emerged.
Mr McCarrick was one of the most prominent US cardinals and is one of the most high-profile Catholic leaders to face abuse claims.
In a statement, the Vatican said Pope Francis had accepted Mr McCarrick's resignation from the cardinalate and had ordered his suspension from the exercise of any public ministry.
The statement also said he would be placed in seclusion "for a life of prayer and penance until the accusations made against him are examined in a regular canonical trial".
His resignation means the titles of Cardinal and "your eminence" are removed, America Magazine editor and Jesuit priest James Martin said on Twitter.
Mr McCarrick's resignation from the cardinalate is the first since 1927, when Father Louis Billot resigned because of political tensions with the Holy See, according to the New York Times newspaper.
It is also the first time that an order to carry out penance and prayer has been made before a Church trial takes place, according to Catholic University legal expert Kurt Martens, quoted by AP news agency.
The Church is now "running out of options if you want to impose a further penalty" after a canonical trial, Mr Martens told the Washington Post.
"I would not be surprised if he gets dismissed from the clerical state," he said.
The Pope appears to "understand the gravity of the situation and further harm to the Catholic Church's status", AP quoted Terence McKiernan from BishopsAccountability.org as saying.
The Vatican's quick action stands in contrast to previous instances where cardinals have faced allegations that they carried out or covered up abuse.
In 2013 Scottish Cardinal Keith Patrick O'Brien resigned as Archbishop of St Andrews and Edinburgh after being accused of sexual misconduct. However he remained in the college of cardinals until he died earlier this year.
Cardinal Bernard Law stepped down as archbishop of Boston in 2002 after reports he had moved paedophile priests between parishes rather than addressing victims' claims. But he was then allowed to take a job at the Vatican, where he worked until 2011. He died in Rome last year.
Mr McCarrick is alleged to have assaulted the teenager while working as a priest in New York in the early 1970s. The claims were made public in June by the current Archbishop of New York, Cardinal Timothy Dolan.
He said an independent forensic agency had investigated the allegations. A review board, including legal experts, psychologists, parents and a priest, then found the allegations "credible and substantiated".
At the time, Mr McCarrick said in a statement that had "no recollection of this reported abuse" and believed in his innocence.
Several more men have since said Mr McCarrick forced them to sleep with him at a beach house in New Jersey, while they studied for the priesthood as adult seminarians. One man has come forward saying he was assaulted while still a minor.
Mr McCarrick has not commented on the more recent allegations.
The alleged abuses may have taken place too long ago for criminal charges to be filed because of the statute of limitations.
It has also since emerged that financial settlements were reached in at least two cases of alleged sexual misconduct with adults involving Mr McCarrick.
They involved "allegations of sexual misconduct with adults decades ago", while Mr McCarrick was working as a bishop in New Jersey, bishops in the state told US media.
He became a priest in 1958 and later worked in New York and New Jersey before becoming Archbishop of Washington between 2001 and 2006.
Despite having officially retired, he has continued to attend events abroad, including those focusing on human rights issues.
He has been heavily involved in the response to allegations of abuse by Catholic priests in the US, local media reports say.
In Washington he was also known for his focus on the plight of Christians and other religious minorities in the Middle East and had a reputation as someone who could work with powerful figures on all sides, US media report.
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