The abusive emails were sent to Ugandan-born Dr John Sentamu after he defended the traditional definition of marriage as a union between one man and one woman in an interview with he Daily Telegraph two weeks ago.
The emails have been forwarded to the police, who are investigating them as hate crimes, the newspaper reports.
A spokesman for the Archbishop said in a statement: "A large quantity of correspondence was received in response to the Archbishop's interview with the Daily Telegraph, which touched on a wide range of issues.
"Amongst many positive emails that he has received, there have been a small number of abusive and threatening emails of a racist nature which North Yorkshire Police are investigating as hate crimes."
In his interview with The Telegraph, Dr Sentamu said that it was not the role of the state to define marriage.
"It is set in tradition and history and you can't just [change it] overnight, no matter how powerful you are," he said.
"We've seen dictators do it in different contexts and I don't want to redefine very clear social structures that have been in existence for a long time and then overnight the state believes it could go in a particular way."
His comments were welcomed by some politicians, including Labour's Jim Dobbin, who warned that more than a hundred MPs could oppose the Government's plans. Conservative MPs Gary Streeter, Jeremy Lefoy and David Burrowes also expressed their opposition.
The Archbishop was criticised for his comments by 70 protesters who gathered outside York Minster last week.
The Bishop of Salisbury, the Rt Rev Nicholas Holtam, expressed his support for a broadening of the definition of marriage to include gay couples.
He told The Times: "All of us have friends, families, relatives, neighbours who are, or who know somebody, in same sex partnerships.
"I'm no longer convinced [that marriage can only be between heterosexual people]. I think same-sex couples that I know who have formed a partnership have in many respects a relationship which is similar to a marriage and which I now think of as a marriage.
"And of course now you can't really say that a marriage is defined by the possibility of having children."