Berquist fell awkwardly when tackling the onrushing Mike Poole in midfield and had to be stretchered off. He had surgery on his knee the following day and it is anticipated that he will be sidelined for approximately four months.
It is a bitter blow for the 28-year-old who signed for Leinster from the Canterbury Crusaders in May on a one-year deal, with the option of a season year.
The absence of the Kiwi, who is now unlikely to play in the Heineken Cup pool stages, leaves Leinster with the 22-year-old Madigan as their main out-half until Jonathan Sexton returns from the Rugby World Cup.
Although Joe Schmidt could also decide to switch the versatile Isa Nacewa from full-back to out-half, a position he has played in before for the province.
Ireland international Luke Fitzgerald is expected to be in contention for selection for the visit of the Scottish side. He sat out last week's match to recover fully from the knee injury he suffered in the opening round.
Second row Steven Sykes has stepped up his rehabilitation from the knee injury he sustained in pre-season and he could come into the mix. A decision on his availability will also be made later in the week.
Over 14,200 tickets have been sold for Saturday's game which will see the usual 'Family Day' activities. Tickets are still available from www.leinsterrugby.ie, Spar (Donnybrook), the Leinster Rugby Store and Ticketmaster outlets nationwide.
Meanwhile, following pre sales which incorporated a special 'Hour of Power' reduced price window on Monday morning, Leinster Rugby are delighted to announce that over 21,000 tickets have already been sold for 'Fever In The Aviva 2' when Leinster take on Munster at the Aviva Stadium on Friday, November 4.
Tickets for the interprovincial derby are on sale now from www.leinsterrugby.ie.