With Leeds' other England and Lions hooker, Steve Thompson, currently away on international duty, Titterell's injury leaves the Yorkshire club with a few problems for this weekend's LV= Cup clash with his former club, Sale Sharks.
Leeds are currently lying in second place in Pool 4 with four points from their 23-9 away win over Bucharest Oaks in Round 1. They then slipped to a 22-13 home defeat to Pool leaders Stade Francais Paris in the second round.
"We are bitterly disappointed for Andy. He will have the operation very soon and I am sure, given his nature and athletic strength, that he will be battling to be back as soon as possible," said Leeds Carnegie Director of Rugby, Andy Key.
"Whilst we have suffered a number of injuries this season, this is only the second time that a serious injury has occurred in training, with Dan White breaking his leg earlier this year, which makes it even more frustrating for Andy.
"Unfortunately in the short term, with Steve Thompson away with England, that only leaves us with Phil Nilsen to cover at hooker. We have two very talented young hookers in Harry Hannan and Scott Freer, but both are coming back from long term injuries.
In the case of Scott, hopefully, he will get some rugby under his belt in the next week and I am sure he will be pushing for inclusion in the first team squad in due course. We have to make sure that we do not rush into a decision in case there are other options out there."
Leeds face Italian side Crociati Rugby at Headingley Stadium in Round 3 on Sunday, 12 November.