Both the Knights and Dragons agreed to the trial with both sides out of the race for the top eight heading into the final round.
It has been endorsed by the NRL competition committee and the ARL Commission and will be reviewed following the end of the season.
A captain's challenge would take heat off the bunker video review system, which has copped criticism from fans and pundits in its first year.
The concept has previously been used in the under-20s competition as well as other sports such as cricket and tennis.
Greenberg said the game was only ready to look at for use in its senior competition because the bunker was in place.
"We trialled this in the 20s for a number of years but we didn't have the technology to support it," Greenberg said. Now we have the technology to use.
"We've been working on this quietly for a couple of months and we're ready to trial it," he said.
How the captain's challenge will work:
* The captain is allowed to challenge a referee's decision in relation to tries and, if challenged, will be sent up to the bunker
* Each team is allowed one incorrect decision per half. There is no limit on challenges if a captain continues to make successful challenges
* Captains will have 20 seconds following a try/no try to contest the decision
* No replays will be shown on a big screen at the ground until the time allowed for requesting a captain's challenge has elapsed
* Captains may challenge a try decision based on groundings, knock-ons, obstruction, double movement, offside, touchline/deadball line, tackle in the air, steals involving two or more defenders, foul play
-AAP