Halfpenny, 24, set a new Lions record of 49 points in the three Tests. Earlier in 2013, his 74 points helped Wales retain their Six Nations title.
Kieran Read and Ben Smith, part of the New Zealand side who have won all their Tests to date in 2013, are among the other players nominated for the award, won last year by All Black Dan Carter.
South African Eben Etzebeth and Sergio Parisse of Italy complete the nominees. The winner will be announced after the autumn window of international matches.
IRB Chairman Bernard Lapasset said: "The IRB Player of the Year Award is the ultimate recognition for achievement on the field from the world's top players and one of the most eagerly anticipated and debated moments of the international Rugby year."
"The list of previous winners reads like a list of the greats of the modern Game and all of our nominees fully deserve their place in the shortlist, displaying great character, ability and brilliance throughout the last 12 months of international Rugby."
The IRB Player of the Year 2013 nominees were selected by the independent IRB Awards panel, chaired by Australia's RWC 1999 winning captain John Eales.
The panel, comprising Will Greenwood, Gavin Hastings, Raphaël Ibanez, Francois Pienaar, Agustín Pichot, Scott Quinnell, Tana Umaga and Paul Wallace, has deliberated on every major Test played in 2013, starting with the opening RBS Six Nations match and culminating with the November internationals.
"The IRB Player of the Year is always a close fought affair and gives the judging panel much consideration and deliberation. The 2013 shortlist was again a tough one to consider and the crowning of the eventual winner will go right down to the wire," said Eales.
In support of the initial nomination process, the public now has the chance to have their say on the shortlist here. The results of the public vote will be considered by the panel when finalising the winner.
The panel will reconvene after the final match on November 30, when the IRB Player of the Year will be selected and announced shortly afterwards. The IRB Coach and Team of the Year 2013 winners will also be announced at this time.
The IRB Player of the Year is one of the most prestigious accolades in Rugby and previous winners have all made a significant contribution to the international Game over the past decade and taken Rugby to new audiences around the world with their skill and talent.
Previous winners include Dan Carter, Thierry Dusautoir, Shane Williams, Bryan Habana, Schalk Burger, Jonny Wilkinson and Richie McCaw with the two All Black centurions the only players to have won the Award on more than one occasion.
The IRB Player of the Year is one of 13 categories of awards this year, including the IRB Coach of the Year, IRB Team of the Year, IRB Sevens Player of the Year, IRB Women's Sevens Player of the Year and IRB Junior Player of the Year.
2012 Dan Carter (New Zealand)
2011 Thierry Dusautoir (France)
2010 Richie McCaw (New Zealand)
2009 Richie McCaw (New Zealand)
2008 Shane Williams (Wales)
2007 Bryan Habana (South Africa)
2006 Richie McCaw (New Zealand)
2005 Dan Carter (New Zealand)
2004 Schalk Burger (South Africa)
2003 Jonny Wilkinson (England)
2002 Fabien Galthié (France)
2001 Keith Wood (Ireland)