FRANKFURT (Reuters) - The chief financial officer of airline Lufthansa <LHAG.DE>, Simone Menne, will join Germany's second-largest drugmaker Boehringer Ingelheim in September, her departure knocking shares in the carrier on Friday.

Lufthansa announced late on Thursday the well-regarded Menne was leaving from Aug. 31 and Boehringer said on Friday she would join the family-run company as CFO on Sept 1.

Shares in the carrier fell 5.5 percent to their lowest since Sept 2015, making it the biggest faller on the German blue-chip index <.GDAXI> as investors worried the company's cost-cutting plans could be thrown off course.

Her departure comes at a time when Lufthansa is grappling with cost challenges, notably on the labor front, and expanding budget unit Eurowings to offer cheaper tickets and defend routes against the likes of Ryanair <RYA.I> and easyJet <EZJ.L>.

CFO for the last four years, Menne has maintained Lufthansa's investment grade credit rating, helped steer the group to record profit and last month she said the group had reached a turning point on bringing down unit costs excluding the price of fuel and currency.

However, the group still needs to strike wide-ranging deals with pilots and cabin crew over pay and conditions, disputes that have seen a series of strikes over the last two years.

Credit Suisse analysts said her departure would deal a blow to the confidence in the airline's cost-cutting efforts, also highlighting how Lufthansa has seen other top executives depart during periods of restructuring, such as former CEO Christoph Franz to Roche in 2013 and CFO Stephan Gemkow to Haniel in 2012.

Gerald Khoo at Liberum said however, her departure was unlikely to impact cost saving plans in the short term, and that a new CFO should be in place in due course.

"Lufthansa does have strength in depth, assuming it does not go for an external candidate as replacement," he told Reuters.

Analysts also cited weak May traffic figures from Thursday as a concern for the carrier, with passenger traffic down 2 percent and its planes less full.

Menne, the first female CFO at a German blue-chip company and who had been with Lufthansa since 1989, has previously spoken of her ambition to become chief executive of a Dax 30 company.

At unlisted Boehringer, she will succeed CFO Hubertus von Baumbach, a member of Boehringer's founding family and who will take over as the group's chief executive in July.

(Reporting by Victoria Bryan and Ludwig Burger; Editing by Arno Schuetze and David Evans)