She has been in her current role leading marketing, comms, IT, ticketing and archives since the start of 2015, having initially joined in 2004.
Woods' exact departure date has not been confirmed. She declined to comment.
Her resignation follows the recent departure of COO James Ainscough.
Woods is listed as one of the three most senior directors of the hall, reporting to CEO Craig Hassall. The new boss joined the Hall in April last year. The hall's president is Jon Moynihan.
The venue and its agency Newsfeed PR scored a hit this week, with with the news that employees have taken Klingon classes after the promised free tickets to two upcoming Star Trek-themed events to anyone ordering in the sci-fi language.
The hall, a registered charity, has also been locked in a legal battle over its governance, based around the issue of trustees being able to sell their tickets at inflated prices.