Full-back Webb has been charged along with Warrington's England forward Ben Westwood with a grade B offence of fighting after both were sin-binned eight minutes from the end of a tempestuous Super League match at the Halliwell Jones Stadium.
Stand-off Pryce is facing a grade A offence of striking with his leg on Wolves scrum-half Richie Myler and has until 11am on Tuesday to submit an early-guilty plea and accept a one-match ban.
Catalan prop Julian Bousquet's appeal against a four-match ban for striking with his shoulder will also be heard on Tuesday.
Meanwhile, Bradford prop Nick Scruton has been accused of striking with his shoulder on Castleford half-back Gareth O'Brien in the fourth minute of his side's 38-12 win over the Tigers on Saturday.
Scruton is also eligible to make an early-guilty plea and avoid a disciplinary hearing.
The players were charged by the Rugby Football League's match-review panel, which issued formal cautions to Wigan prop Gil Dudson and Huddersfield full-back Scott Grix for kicking out at each other during the Giants' 22-10 win on Saturday.
