Henson, a Lion in 2005, has been named in Warren Gatland's 45-man preliminary World Cup squad which will later be cut to a final 30 ahead of the tournament.
But Henson has be named as The Bachelor in a UK version on the popular America reality show.
The WRU said Henson was fulfilling prior work commitments and will follow a personalised training programme until linking up with the squad on June 30.
"The squad are currently committed to personalised training programme in and around prescribed holiday periods, meaning some are already on site at WRU headquarters and others have been given regimes to follow away from camp depending on their personal requirements, like Gavin, or are resting or undergoing rehab," said a WRU spokesperson.
"Gavin is fulfilling a work commitment which was in place before he was selected for national squad duty and doing so in the full knowledge of the Wales management team.
"He has already undergone periods of extra conditioning work and is maintaining constant contact with the WRU's head of strength and conditioning Adam Beard."
It is not the rugby player's first foray into the world of reality TV, having previously featured on BBC One's Strictly Come Dancing and on ITV1 adventure series 71 Degrees North.
In the latest appearance, contestants will compete to be chosen has Henson's ideal partner.
The hopefuls will live together in a villa in southern Europe with Henson based in a nearby bachelor pad.