Spark said in a statement that coverage would begin on Monday at 1.20am (11.30pm Sunday AEDT) with the match between Reading and current league leaders, Manchester United.
This would be followed by the game between the second-placed Arsenal and Manchester City.
Two matches will be streamed live each week for the rest of the season, with a weekly highlights show and replays available on demand.
"Having the Barclay FA Women's Super League on our platform means New Zealand football fans now have the chance to watch the best female footballers that the world has to offer week in, week out.
"Streaming the Super League will also mean a few more Kiwi families, local clubs, friends and communities will get to see their daughter, sister or friend play top-class UK football with some of our best New Zealand football exports lining up amongst the teams.
"Our homegrown talent in the league includes the likes of Kiwi goalkeeper, Erin Naylor suiting up for Reading FC, her Football Fern teammate Ria Percival running out for Tottenham Hotspur and seasoned Football Fern campaigner Rebekah Stott appearing for Brighton & Hove Albion.
"Knowing our Kiwi footballing community now have a place to watch is great – we wish the players all the very best and cannot wait to deliver the action across New Zealand households to inspire the next generation of Football Ferns."
FA's Broadcast and Media Rights lead Tom Gracey said of the deal: "We're delighted to be able to bring a further broadcast deal to our growing international audience.
"Spark Sport's interest is another sign of the growing interest in the Barclays FA Women's Super League and it's great news that the co-hosts of the next FIFA Women's World Cup can now watch some of their international players through one of its main streaming services."