In the Championship, Featherstone Rovers' home meetingwith Haolifax and Dewsbury Rams' trip to Swinton Lions were also called off.
Rhinos' game at Huddersfield Giants was postponed at around 11.30 with Trinity calling off their clash with Catalans Dragons shortly afterwards.
With Catalans in the country, Trinity were hoping to rearrange their game for tomorrow.
The decisions came after Storm Ciara lashed Yorkshire with torrential rain and destrutive winds.
Giants staff were initial hoeful the game would go ahead, but an inspection was held at 11.15am and a statement on social media said: "Huddersfield Giants can confirm that today's game has been postponed due to health and safety issues surrounding the perimetre of the stadium."
It added: "All tickets purchased will remain valid for the rearranged fixture and more details on the rescheduling will be announced in due course."
Hunslet were confident their Coral Challenge Cup tie at home to Coventry bears will go ahead.
However, their opening Betfred League One game at Keighley Cougars in seven days' time is likely to be postponed..
Keighley's Challenge Cup tie against Newcastle Thunder was called off today and is expected to be rearranged for next Sunday
Yorkshire Carnegie's rugby union Championship home meeting with Ampthill was postponed on Sunday morning.
Bradford Bulls' game at York City Knights, scheduled to be the last rugby match at Bootham Crescent, was among others to be postponed.