In an open letter published on the school's website, architecture dean Kent Kleinman described Meier's behaviour as "unacceptable" and said he would review all previous donations from the architect.
Kleinman said the school was cancelling an event due to be held in Meier's honour next week and was reviewing previous donations by the Pritzker Prize-winning architect.
"I am deeply disturbed to learn of the allegations of sexual misconduct by Richard Meier," said Kleinman, whose full title is Gale and Ira Drukier dean of architecture, art and planning.
"As one of our most well-known alumni, Richard Meier has been associated with Cornell University and the College of Architecture, Art, and Planning through his gifts that support students and faculty," he said. "Although he has apologised, the reported behaviour is unacceptable."
Cornell rejects donation from Meier
Meier, 83, completed his bachelor 's degree in architecture in 1956 and has endowed the school, part of the private Cornell University located at Ithaca in New York state, with numerous gifts since.
"We will decline his new gift to name the chair of the Department of Architecture, and we are cancelling the event that had been planned for next week to celebrate the gift," Kleinman's statement continued.
"We will swiftly explore what additional actions are appropriate with regard to endowments for professorships and scholarships previously donated to Cornell."
The move follows a report in the New York Times yesterday, 13 March 2018, detailing allegations of inappropriate sexual behaviour towards five women.
The allegations, four of which come from former employees at Richard Meier & Partners.
Meier apologised for his behaviour
Shortly after, Richard Meier & Partners issued a statement announcing that the architect would be taking a six-month leave of absence from the company. The statement contained an apology from Meier "to anyone who was offended by my behaviour".
Meier has retained strong ties with his alma mater since graduating. In 2008 he completed Weill Hall, a life-sciences research facility at the campus and has made numerous donations to the architecture school.
Awards and professorships he has sponsored include the Ana Meier Graduate Scholarship, set up to create opportunities for promising female applicants to the architecture programme. Most recently, he offered to fund the new chair for the school's architecture department.
Architect has won Pritzker Prize and AIA Gold Medal
Meier founded his architecture practice in 1963, and his acclaimed portfolio includes the Getty Centre in Los Angeles, the Barcelona Museum of Contemporary Art and the City Hall in The Hague.
The architect remains hugely influential and ranked at 71 on Dezeen Hot List 2017. Meier spoke to Dezeen in 2016 in an exclusive interview. "I'm the only one in the office who doesn't have a computer," he said at the time. "I give a drawing to someone and they put it on their computer. Then I mark it up."
Claims follow growing scrutiny of workplace harassment
The Meier allegations follow the Harvey Weinstein scandal and the resulting #MeToo and #TimesUp movements, which have increased awareness of sexual inequality in the workplace.
Dezeen columnist Anna Winston explored sexism and harassment in architecture last October, wondering whether there could be a Harvey Weinstein in the profession.
In November, Dezeen surveyed the world's 100 biggest architecture firms and revealed "shocking" gender imbalance at the top management tiers. Last week we launched an initiative to improve equality called Move the Needle.
Photograph of Richard Meier is by Silja Magg.