The club says the leak was “major” and in the northern section of the stadium.
But they fully expect their clean-up operation to be completed in time for the Premier League game with Aston villa a week on Sunday.
They are also hopeful all will be rectified by the time they face Bologna on Saturday (3pm).
However, should any of the affected areas not be cleared in time, they have told fans they have a contingency plan to re-locate fans where necessary.
They will write directly to anyone affected by close of play on Friday to provide an update.
Albion said: “The club’s staff and contractors have been working since the early hours of this morning on a large-scale clear-up operation which we fully expect to be completed before our season opener against Aston Villa a week on Sunday.
“We also remain hopeful most of the affected areas will be operational in time for Saturday’s second home pre-season friendly against Bologna.”
They added: “We apologise for any inconvenience this issue might cause and look forward to seeing you at the Amex on Saturday.”
Tickets for the North Stand remained on sale on Thursday afternoon.
Fans are reminded the South Stand is for away fans only.