Joyce said he had been described in one email as "foreign filth" and warned that all his "evil plans ... will come back to you very swiftly".
He has hired extra private security and the threats are being investigated by both the federal and New South Wales police.
Describing the threats as vile and cowardly, Joyce sent a memo informing the airline's 35,000 staff of "intimidation and bullying" and warning that anyone involved would face serious consequences.
He denied union suggestions the threats were fabricated by Qantas as part of a public relations campaign and said he had gone public to bring them to a halt.
"For me what's important is that we have to stop the intimidation and the bullying that's taking place in the workplace," he told ABC radio.
"Very clearly, as a consequence of the industrial action that's been taken we've had a number of management and other employees who have experienced destruction to their property, have experienced threats, have experienced letters at home ..."
Transport Workers Union national secretary Tony Sheldon said the union had also received "threats and aggressive messages" in the past few weeks, and had complained of "thugs" being sent to members' homes with letters from Qantas demanding their return to work.
Qantas denied intimidation and said it was legally required to inform staff of its response to the union's action.
"We are progressing our complaints to the Fair Work Ombudsman concerning the 'midnight door-knocks' and threatening letters our members and their families got hours before the first stoppage," Sheldon said.
"We are also gathering evidence of members being refused ordinary entitlements and locked out in retaliation for participating in last week's one-hour stoppage."
Sheldon said the union had taken the threats it received to the police, rather than releasing them to the media as Qantas had done.
"The union is curious as to the chain of events surrounding Qantas' allegations. Who found out first, the media or the police? Has the very public airing of these allegations compromised an investigation?"
Licensed Aircraft Engineers Association federal secretary Steve Purvinas said the airline's decision to go public was "a little bit fishy" and it was possible the threats had been made up to boost public sympathy for Qantas.
Both Sheldon and Purvinas said anyone involved in making threats should feel "the full force of the law".