The company, in which German billionaire Susanne Klatten owns a 28% stake alongside smaller stakes held by carmakers BMW and Volkswagen, also warned profit this year would fall short of a forecast it affirmed just last week.
SGL shares fell 32% to 3.68 euros in morning trade, set to mark their biggest one-day decline. The fall put the company's market value below 450 million euros, in what a local trader described as an "absolute disaster" for investor confidence.
BMW and Volkswagen tussled for control of SGL in 2011, driving its market value above 3 billion euros in anticipation that carbon fibre-reinforced parts would be used more widely in electric vehicles.
But the business failed to live up to expectations.
In a statement late on Wednesday, SGL - whose carbon fibre is used in auto parts and wind turbines - said its forecasts for the 2020-2022 period had become obsolete and restructuring measures were being considered.
It also said it expected adjusted operating profit this year would fall 10 million euros (9.2 million pounds) below last year's level of 65 million euros instead of being flat as previously expected.
Cost overruns in a large order - for rotor-blade materials from a wind energy company - were partly to blame for the bleaker outlook, a spokesman added.
The wind energy industry is being weaned off the generous state subsidies on which it was built.
Turbine maker Vestas on Thursday said earnings were hit by competitive markets and tariffs while rival Nordex, in which Klatten also holds a stake, has coped better with price pressure this year.
Christian Obst, an analyst at brokerage Baader Helvea, said Klatten - who also owns a stake in BMW that she inherited from her father Herbert Quandt - could opt to buy out SGL. A spokesman for Klatten declined to comment on her plans with SGL.
SGL said CEO Juergen Koehler would step down at the end of the month with Klatten, head of the non-executive supervisory board, showing "complete respect and understanding for this decision". SGL did not name a successor.
The company's graphite and carbon products go into semiconductor production gear, anodes of lithium-ion batteries as well as lightweight parts in BMW electric vehicles and luxury sedans.
A business that makes graphite electrodes for steel furnaces - once SGL's major cash generator - was sold in 2017 after it came under pressure from Chinese rivals.
(Additional reporting by Patricia Weiss; Editing by John Stonestreet, Michelle Martin and Deepa Babington)
By Ludwig Burger