Many clubs are facing a major financial crisis and have not paid salaries for several months.
The footballers' union says the strike will go on until the players received what they are owed.
The strike involves players of more than 200 Argentine clubs.
The two matches postponed were Rosario Central v Godoy Cruz, in the city of Rosario, and San Lorenzo v Belgrano, in Buenos Aires.
The crisis began after senior officials at the Football Association (AFA) were implicated in a corruption scandal involving television broadcasting rights.
The season should have resumed a month ago after the summer recess.
But the crisis led the AFA to delay the start until this Friday.
To try to avoid the strike, the government of Mauricio Macri made a $22m (Â£18m) payment on Thursday to the Argentine Football Association.
The money was owed as compensation for the cancellation of a contract with the government, which held the broadcasting rights until this year.
But the players' union says the money is not enough.
They said most club presidents had spent and borrowed more money than they should have.
The death in 2014 of Julio Grondona, who was president of the Argentine Football Association for 35 years, triggered the crisis.
He was also vice-president of Fifa, the world football's governing body.
The United States authorities who investigated corruption at Fifa labelled Mr Grondona "the number one conspirator".
But analysts in Argentina say he guaranteed the functionality of Argentine football.
Many believe, however, that his absence will allow a perhaps tortuous but necessary clean-up of the game, says the BBC's Daniel Pardo in Buenos Aires.

Seventh-placed Vikings went into the break 8-0 ahead thanks to two tries from Corey Thompson.
Liam Farrell's converted score brought Warriors back to within two against a side who defended stoutly despite at one stage having two in the sin-bin.
Wigan turned down a late chance for goal, but the visitors held out.
Shaun Wane's side need only one point to confirm a top-four finish, but decided against trying to draw the match when they won a 79th-minute penalty.
They decided to run it and, after it came to nothing, Widnes saw the clock down.
Wigan: S Tomkins, Charnley, Gelling, Sarginson, Tierney, Williams, Shorrocks, Sutton, Powell, Flower, Farrell, Bateman, Isa.
Replacements: Tautai, Gildart, Nuuausala, Bretherton.
Widnes: Hanbury, Thompson, Dean, Runciman, Marsh, Mellor, Brown, Burke, White, Buchanan, Whitley, Houston, Cahill.
Replacements: J Chapelhow, Dudson, Heremaia, Farrell.
Referee: Phil Bentham (RFL)
The Argentine Football Association has postponed two top division matches that were due to take place on Friday following the collapse of negotiations to call off a players' strike.
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Widnes Vikings produced a superb defensive display to beat Wigan and leave Warriors still waiting to confirm their Super League play-off place.