Hines has been left out to enable him to spend time in his native Australia helping care for his sick mother-in-law but the door has been left open for him to join the tour if he wishes to at a later stage.
"He's going back to see his wife, who has been over in Australia nursing her sick mother," said Scotland head coach Andy Robinson.
"It's time for him to be there and if Nathan feels he can come across to Argentina at a later stage then we will leave that open for him to be able to do so."
Robinson, who was part of the Lions' coaching staff in Australia nine years ago, has selected a largely familiar squad for the Two-Test series against the Pumas.
Robinson keeps faith with the entire 22 that recorded a famous win over Ireland in the final Six Nations tie at Croke Park two months ago and, unlike England's Martin Johnson, who has selected nine potential debutants in his 44-man summer squad, Robinson has chosen just the one new cap in Edinburgh's Jim Thompson.
The former Scotland Sevens star has represented his country at A level and has impressed in the Magners League this season.
"We are really looking forward to playing against Argentina," added Robinson.
"We have a lot of respect for the way the game is played there and we want to improve upon our success in our most recent game in the Six Nations.
"As well as our two Test matches in Argentina we will prepare for those contests with our game at Murrayfield against a Japan Select.
"In addition there are matches against Georgia, Namibia and Argentina Jaguars for Scotland A in the IRB Nations Cup, so from my perspective we are playing six Test matches this summer and that will be reflected when we announce the Scotland A squad next week."
Sean Lineen, the Glasgow head coach, will lead Scotland A in their defence of the Nations Cup, which was won when Robinson was at the helm in Bucharest last June.
From the squad that defeated Uruguay, Russia and their French counterparts last year, Alex Grove, Richie Vernon and Kyle Traynor went on to win Scotland caps in the past year, underlining Robinson's stance on the importance of the Scotland A team.
Scotland's summer fixtures in Argentina
First Test - Saturday, June 12, Tucuman, kick-off 7.45pm BST
Second Test - Saturday, June 19, Mar del Plata, kick-off 7.45pm BST
The Scotland squad depart on Friday, June 4.
Forwards: John Barclay, Johnnie Beattie, Kelly Brown (all Glasgow Warriors), Alasdair Dickinson (Gloucester), Ross Ford (Edinburgh), Richie Gray (Glasgow Warriors), Jim Hamilton, Allan Jacobsen (both Edinburgh), Alastair Kellock (Glasgow Warriors), Scott Lawson (Gloucester), Moray Low (Glasgow Warriors), Alan MacDonald (Edinburgh), Euan Murray (Northampton Saints) and Alasdair Strokosch (Gloucester)
Backs: Mike Blair (Edinburgh), Chris Cusiter CAPTAIN (Glasgow Warriors), Simon Danielli (Ulster), Nick De Luca (Edinburgh), Max Evans (Glasgow Warriors), Phil Godman (Edinburgh), Alex Grove (Worcester Warriors), Sean Lamont (Scarlets), Rory Lawson (Gloucester), Graeme Morrison, Dan Parks (both Glasgow Warriors), Hugo Southwell (Stade Francais), Jim Thompson (Edinburgh)