Hodge and New South Wales left-hander Simon Katich would battle it out for the remaining place in Australia's strong batting line-up after Darren Lehmann and Shane Watson were ruled out through injury, Cricket Australia said in a statement.
Lehmann had been hoping to keep his place in the Test squad after he was left out of the one-day team last month but will undergo surgery next week on an injured shoulder.
Hodge has amassed an impressive total of 735 runs in the Australian domestic series, including a double century.
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"He has presented an irresistible case to be part of this tour and if he gets the opportunity, we feel confident that he can do a good job for Australia," he said.
Hodge is the only uncapped player in the squad, although he was a member of the party which toured India last year.
The decision to name a 13-man squad also means Shane Warne will be the only specialist spin bowler on the tour, with Stuart MacGill overlooked despite good performances in Australia's Test series win over Pakistan this year.
Paceman Brett Lee was included and will be vying for a place in a strong fast bowling line-up alongside Glenn McGrath, Jason Gillespie and Michael Kasprowicz.
The first Test starts in Christchurch on March 10.
Australia: Ricky Ponting (captain), Adam Gilchrist, Michael Clarke, Jason Gillespie, Matthew Hayden, Brad Hodge, Michael Kasprowicz, Simon Katich, Justin Langer, Brett Lee, Damien Martyn, Glenn McGrath, Shane Warne.
