Hearts are keen to reduce prices to increase attendance for the fourth-round match, scheduled to kick-off at 2pm on Sunday, January 9. However, St Johnstone have requested a pricing policy in line with SPL games as they are entitled to a 50 per cent share of gate receipts.
It is understood officials at Tynecastle planned to charge as little as 17 in the Wheatfield, but their counterparts at McDiarmid Park want tickets sold at 26 as they would be for a league encounter.
St Johnstone's stance has enraged Hearts, who will now take the unprecedented step of closing the Wheatfield Stand completely. Tickets will cost a maximum of 22 in other areas of the stadium when they go on sale on Tuesday.
A spokesperson for the Edinburgh club said: "Our staff have been negotiating with St Johnstone on an almost daily basis since the afternoon of the Scottish Cup draw.
"We've moved our positions on a couple of occasions to try and meet St Johnstone's pricing expectations, and we believed we had reached an acceptable-to-all-parties compromise today.
"We have, however, to respect St Johnstone's decision to charge much higher prices, and we reiterate we'll afford them a very warm welcome to Tynecastle."
Geoff Brown, the St Johnstone chairman, said: "If you look at the draw, this stands out as probably the most attractive fixture of the lot. So why cut the prices? Those are the prices you'd have for a league game between the sides. Why should the cup be any different?"