Henry was expected to be in control of the Baa-baas visit, but – according to allblacks.com – the former Wales and Lions coach is now "concentrating on the process of applying for the All Blacks job that has been advertised in the wake of New Zealand's semi-final exit from the World Cup".
Williams has is a former Samoa, Hurricanes and Auckland coach and is currently employed by the Auckland Rugby Union.
Barbarians President Ken Eglington said England had indicated they would field the same 22 that beat Australia in the World Cup Final.
He said Henry, as a Barbarians club member, had been involved in team selection and would continue to help with preparations.
Barbarians organisers are still working through the make-up of their team, but it is unlikely to contain any current All Blacks and will be a mix of players from New Zealand, Australia, South Africa and Fiji. Several of the Kiwis are expected to be overseas-based players.
The NZ Baa-baas are expected to confirm their full 22-man squad shortly.
Eglington said progress indicated a "good" forward pack was being lined up and the famous red jersey would also be worn by at least one uncapped player, as is the tradition of the club.
The Barbarians' last outing was a victory over New Zealand Maori at Albany last year.
Meanwhile, Twickenham has sold out for the match, the first home appearance of the victorious England side that returned to London on Wednesday after their successful campaign in the Rugby World Cup Australia.