Born in Germany, Abetz emigrated to Australia as a small child, when his father came to work for Tasmania's Hydro Electric Commission. He was educated at the University of Tasmania and was a barrister and solicitor before entering politics. A former national president of the Australian Liberal Students' Federation, he was state president of the Tasmanian branch of the Liberal Party from 1990 to 1994.
The youngest of six children, Abetz emigrated from Germany to Australia with his parents in 1961. His father, a radio technician, came to Australia to work for Tasmania's Hydro Electric Commission, which had advertised for skilled workers in German newspapers. Another one of the Abetz children is Peter Abetz, who was the Liberal member for Southern River in the Legislative Assembly of Western Australia from the 2008 state election until 2017.
Abetz is a great-nephew of Otto Abetz, a Brigadier General in the SS, who was Nazi Germany's ambassador to Vichy France from 1940 to 1944 and was sentenced to 20 years for war crimes relating to the deportation of French Jews to the death camps. Eric Abetz was about 3 months old when Otto Abetz died.
Abetz is married to Michelle.
Abetz studied at Taroona High School, Hobart Matriculation College and the University of Tasmania, earning degrees in law and arts in 1981. In 1980–1981, he became the only Tasmanian to become national president of the Australian Liberal Students' Federation, during which time he came into political conflict with Nick Sherry and Sue Mackay, both later to be Australian Labor Party senators.
He won preselection as a candidate for the Senate in the 1993 election but did not win a seat. He was then chosen to fill the casual vacancy caused by the resignation of Brian Archer in 1994, and was elected in his own right at the subsequent 1998 election and re-elected in 2004 and 2010. Abetz was Parliamentary Secretary to the Minister for Defence 1998–2001 and was Special Minister of State from January 2001 until 2006.
He has served as Chairman of the Native Title and the Aboriginal and Torres Strait Islander Land Fund Committee and Chairman of the Senate Legal and Constitutional Affairs Legislation Committee. He also served as Chairman of the Attorney-General and Justice Government Members' Committee.
He was a member of a Parliamentary Delegation which visited France and Belgium in June and July 1997, and made an official visit to the United Kingdom in September 1999.
He was Minister for Forestry from a reshuffle of the Howard ministry in January 2006 until its defeat at the 2007 election. He commenced his portfolio by attacking the Australian Greens and environmentalists in general as anti-Australian. He described the campaign against woodchipping as "akin to treason" and branded the Greens an "extreme left" party. This allowed him to position the government's priorities as mainstream issues which both major parties wanted action on.
He was appointed Minister for Employment in the Abbott Government in September 2013 and oversaw the drafting of legislation to reestablish the Australian Building and Construction Commission, establish a Registered Organisations Commission following the Craig Thomson Affair as well as commencing the Royal Commission into trade union governance and corruption and Fair Work Act Review. Abetz also designed and implemented the Government's Jobactive Employment Services Reforms.
Abetz is a Christian and a member of the Christian Reformed Churches of Australia. Throughout his political career he has been variously associated with conservative groups, including the Association of Christian Parent Controlled Schools, Salt Shakers, Focus on the Family, Lyons Forum, Endeavour Forum, Family Council of Victoria, Fatherhood Foundation, Australian Christian Lobby, Australian Family Association and Right to Life Australia. Abetz is an opponent of same-sex marriage, and in a 2015 interview on 2UE said arguments comparing discrimination against mixed-race couples to same-sex couples were "completely debunked by Justice Clarence Thomas, the negro American on the Supreme Court".
Abetz is quoted as saying of Joe de Bruyn, National President of Labor's largest trade union, "he is a role model of trade union officialdom. He is the type of official that gives trade unionism a good name."
In August 2014 Abetz received criticism from the media and politicians such as Greens Adam Bandt for making claims of a link between abortion and breast cancer when appearing on The Project. He had been on The Project to discuss his association with the World Congress of Families.
Abetz was dropped from the First Turnbull Ministry upon the ascension of the Turnbull Government, with George Brandis succeeding Abetz as Leader of the Government in the Senate. In the three days where Abetz was Prime Minister Malcolm Turnbull's representative in the Senate Abetz said "The King is dead, long live the King" in reference to the leadership change.
In mid-2009 Abetz was a central figure in the OzCar affair, which involved allegations that Prime Minister Kevin Rudd and Treasurer Wayne Swan had improperly given favourable treatment to a car dealer, John Grant, who was a friend of the Prime Minister. At a Senate inquiry on 19 June, Abetz asked a series of questions of a Treasury official, Godwin Grech, who testified that he had a "recollection" that a member of Rudd's staff had sent him an email in February, asking that he provide preferential treatment to Grant. Abetz read out the text of what he said was an email, which purported to ask for preferential treatment for Grant. On 4 August 2009, Grech admitted that he had forged the email. Abetz then issued an apology, saying: "I am not only sorry to Malcolm Turnbull but to the Australian people and any anguish that may have been occasioned to Kevin Rudd and other people."
On 30 July 2010, Tasmanian resident John Hawkins lodged an objection to Abetz's nomination for re-election, alleging that Abetz still held dual citizenship of both his birthplace, Germany, and Australia and thus was ineligible under Section 44 of the Constitution of Australia. Hawkins subsequently withdrew the petition to the High Court of Australia after receiving appropriate documentation, and the High Court never heard the claim.